id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_4_4_300
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3) - 2)/(-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3))) + 1)/(-2((-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3) - 2)/(-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3))) + 1) and g(x) = (-2((-2(4((-1x + 2)/(-3x + 4))^2 - 2) + 2)/(2(4((-1x + 2)/(-3x + 4))^2 - 2))) + 3)/(1((-2(4((-1x + 2)/(-3x + 4))^2 - 2) + 2)/(2(4((-1x + 2)/(-3x + 4))^2 - 2)))) between the vertical lines x = 0.8 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.9
|
math
|
train
|
math_algebra_func_area_level_4_4_301
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-5(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)^2 - 4(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)))/(2(-5(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)^2 - 4(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)) + 2), g(x) = 2(3sin(3π(3(1|x + 1| + 3)^2 - 2(1|x + 1| + 3) - 1) + 1) - 2)^2 + 1(3sin(3π(3(1|x + 1| + 3)^2 - 2(1|x + 1| + 3) - 1) + 1) - 2) + 1, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_4_4_302
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-1(2|(1((-1x - 3)/(1x))^2 - 5((-1x - 3)/(1x)) + 3) + 2|)) - 5, g(x) = -3cos(3π(4(2(-3|x + 3| - 3)) + 5) + 3) - 3, x = -1.2, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_303
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-2|(-1|(-1(1e^(-1x) + 1)^2 + 2(1e^(-1x) + 1) - 4)| + 2) + 2| - 3) + 1| + 2 and g(x) = -3|(1|(2(-3sin(1πx - 3) - 2) - 3) + 2|) + 2| - 3 from x = 4.6 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_304
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(4(1(3(2|x| - 3)^2 - 2(2|x| - 3) + 2) - 3)^2 - 5) + 1 and g(x) = -2|((1(-3(-3x^2 - 4x + 2)^2 - 5(-3x^2 - 4x + 2) - 1) + 1)/(3(-3(-3x^2 - 4x + 2)^2 - 5(-3x^2 - 4x + 2) - 1) + 1)) - 2| - 1 between the vertical lines x = -1.9 and x = -1.7999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_305
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π((-2(3(-1|((1x + 2)/(1x)) - 3| - 1) - 5) + 3)/(3(3(-1|((1x + 2)/(1x)) - 3| - 1) - 5) + 1)) + 3) - 1 and g(x) = -1(3e^(-2(1(-5x + 1)^2 - 2(-5x + 1))))^2 - 1 between the vertical lines x = -0.2 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
86.1
|
math
|
train
|
math_algebra_func_area_level_4_4_306
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2((3(-3cos(2π((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) - 2)/(3(-3cos(2π((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) + 2)) + 1)/(1((3(-3cos(2π((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) - 2)/(3(-3cos(2π((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) + 2))) and g(x) = 1(2(1(-3sin(3πx) + 3) + 2) + 5)^2 - 5(2(1(-3sin(3πx) + 3) + 2) + 5) - 5 from x = -1.2 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
213.5
|
math
|
train
|
math_algebra_func_area_level_4_4_307
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(1((-2(-1cos(1π((3x - 3)/(2x + 3)) - 2) - 2) - 1)/(1(-1cos(1π((3x - 3)/(2x + 3)) - 2) - 2) + 3)) + 2) - 3| and g(x) = (-1((1(1|(-1x^2 + 3x - 1) - 3| - 3) - 1)/(2(1|(-1x^2 + 3x - 1) - 3| - 3) + 3)) + 3)/(-3((1(1|(-1x^2 + 3x - 1) - 3| - 3) - 1)/(2(1|(-1x^2 + 3x - 1) - 3| - 3) + 3)) + 1) from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
213.2
|
math
|
train
|
math_algebra_func_area_level_4_4_308
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(3|(-1((1(2x - 5) + 3)/(1(2x - 5) + 2))^2 + 2((1(2x - 5) + 3)/(1(2x - 5) + 2)) + 1) + 3| - 3) - 5, g(x) = 1|(2(-1|((1x - 1)/(2x + 2))| - 1)^2 - 3(-1|((1x - 1)/(2x + 2))| - 1) + 3) - 3|, x = 1.3, and x = 1.4000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.9
|
math
|
train
|
math_algebra_func_area_level_4_4_309
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((-2(-3|(-2cos(3π(-3x - 2) + 3) - 2) - 3| - 2) + 1)/(1(-3|(-2cos(3π(-3x - 2) + 3) - 2) - 3| - 2) - 2)) + 1| and g(x) = 2cos(2π(-1(1((2x - 2)/(2x - 3)) + 4)^2 - 2(1((2x - 2)/(2x - 3)) + 4)) + 3) - 2 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_310
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-5((2(1(2x + 3)^2 + 3(2x + 3) + 3))/(1(1(2x + 3)^2 + 3(2x + 3) + 3))) + 5) - 3)/(-2(-5((2(1(2x + 3)^2 + 3(2x + 3) + 3))/(1(1(2x + 3)^2 + 3(2x + 3) + 3))) + 5) + 3) and g(x) = 3sin(3π(-2(1((-2x - 3)/(1x + 2)) + 1) + 4) + 2) - 2 from x = -1.2 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_311
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(1sin(2π(-2|(5(3x^2 + 5x - 5) - 1) + 1|) - 3) + 2) - 2| - 3 and g(x) = -3(1(2(1x)^2 - 2(1x) + 2)^2 - 3(2(1x)^2 - 2(1x) + 2) - 1) + 1 between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_312
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(3|(4(3sin(3π(-3|x + 2|) - 2) - 3)^2 - 4(3sin(3π(-3|x + 2|) - 2) - 3) - 1) - 2| - 3) + 5 and g(x) = 2(1|(-2|(-4x^2 - 4x + 2) - 3| - 2) + 3| - 1) between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.5
|
math
|
train
|
math_algebra_func_area_level_4_4_313
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(1π(-2|(2(4(-2x)^2 + 3(-2x) - 1)^2 - 1(4(-2x)^2 + 3(-2x) - 1) - 3) - 1| + 1) + 3) + 3, g(x) = (-1((-3((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) + 3)/(-2((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) - 2)) + 2)/(-1((-3((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) + 3)/(-2((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) - 2))), x = 2.5, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_314
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-1(2|((-3(-3x^2 + 4x + 4) + 1)/(-3(-3x^2 + 4x + 4) + 2)) + 3|) + 2) + 3)/(3(-1(2|((-3(-3x^2 + 4x + 4) + 1)/(-3(-3x^2 + 4x + 4) + 2)) + 3|) + 2) + 2), g(x) = -1(5(1(1|x| - 2) - 1) - 5)^2 - 3(5(1(1|x| - 2) - 1) - 5) + 5, x = -4.3, and x = -3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.3
|
math
|
train
|
math_algebra_func_area_level_4_4_315
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(2|((3(5(1x^2 - 3x - 4) + 5) + 1)/(2(5(1x^2 - 3x - 4) + 5) - 1))| - 2) - 2)/(-3(2|((3(5(1x^2 - 3x - 4) + 5) + 1)/(2(5(1x^2 - 3x - 4) + 5) - 1))| - 2) + 4) and g(x) = 2(2cos(3π(1((-3x - 1)/(-2x - 3))^2 + 3((-3x - 1)/(-2x - 3)))) + 1) + 2 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_316
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-1|(-4(2(-3cos(3πx - 1) + 3) - 4)^2 + 1(2(-3cos(3πx - 1) + 3) - 4) - 1)| - 3) + 1 and g(x) = (-1(-3cos(3π(-1|(5x + 5) - 1| - 2) - 3) - 2) + 1)/(3(-3cos(3π(-1|(5x + 5) - 1| - 2) - 3) - 2) - 1) from x = 0.6 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
187.6
|
math
|
train
|
math_algebra_func_area_level_4_4_317
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(1(-2(1|(5x + 4) - 1| + 3)^2 + 4(1|(5x + 4) - 1| + 3) + 2) + 5) - 1| + 1 and g(x) = 5((-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 1)/(-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 3))^2 - 5((-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 1)/(-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 3)) - 5 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_318
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(2((-1(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))/(2(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))) - 4) - 1)/(-3(2((-1(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))/(2(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))) - 4) + 2) and g(x) = (-1(3(-2|(1|x - 3| + 2) - 3| + 3) - 5) - 3)/(2(3(-2|(1|x - 3| + 2) - 3| + 3) - 5)) between the vertical lines x = 1.1 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.1
|
math
|
train
|
math_algebra_func_area_level_4_4_319
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-2sin(1π((-1(5((1x - 3)/(-2x + 3)) + 1) - 3)/(-3(5((1x - 3)/(-2x + 3)) + 1) + 4)) - 2)) and g(x) = 1sin(3π((3(-4(1x - 2) + 5) - 3)/(-3(-4(1x - 2) + 5) - 3))) + 2 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_320
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-1|(-2|((2(-4x + 4) - 2)/(-3(-4x + 4))) - 1| + 3) - 3|) - 1, g(x) = -2|((-2(5(3x^2 + 1x)^2 - 2(3x^2 + 1x) + 4) + 3)/(2(5(3x^2 + 1x)^2 - 2(3x^2 + 1x) + 4) + 1)) + 1| + 2, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.0
|
math
|
train
|
math_algebra_func_area_level_4_4_321
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-4(2|(1cos(3π(3|x - 3| - 2) - 2) - 1) + 2|)^2 + 3(2|(1cos(3π(3|x - 3| - 2) - 2) - 1) + 2|) + 1) - 1)/(-1(-4(2|(1cos(3π(3|x - 3| - 2) - 2) - 1) + 2|)^2 + 3(2|(1cos(3π(3|x - 3| - 2) - 2) - 1) + 2|) + 1) - 2) and g(x) = 2cos(1π(-3|((-3((-2x - 3)/(-3x + 2)) + 3)/(3((-2x - 3)/(-3x + 2)) + 3)) - 2| + 3) - 3) + 3 from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_322
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(1|((2((2(-3|x + 3| - 1) - 1)/(1(-3|x + 3| - 1) - 3)) + 2)/(-2((2(-3|x + 3| - 1) - 1)/(1(-3|x + 3| - 1) - 3)) + 3)) + 1| + 2) - 1| - 2, g(x) = (-2(3sin(2π(3(-1|x - 3| - 3) + 1) - 3)) + 2)/(2(3sin(2π(3(-1|x - 3| - 3) + 1) - 3)) + 2), x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_4_4_323
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(5(1|(-3(3cos(1πx - 2) - 1) + 4) + 1| - 1)^2 + 3(1|(-3(3cos(1πx - 2) - 1) + 4) + 1| - 1) - 1) - 2)/(3(5(1|(-3(3cos(1πx - 2) - 1) + 4) + 1| - 1)^2 + 3(1|(-3(3cos(1πx - 2) - 1) + 4) + 1| - 1) - 1) + 2) and g(x) = -1|(-2|(-1(-4x - 4) - 2) + 3|) + 3| + 1 between the vertical lines x = 2.8 and x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
75.6
|
math
|
train
|
math_algebra_func_area_level_4_4_324
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(1((-3(2cos(1π(-3|x + 3|))) - 2)/(2(2cos(1π(-3|x + 3|))) + 1))^2 - 3((-3(2cos(1π(-3|x + 3|))) - 2)/(2(2cos(1π(-3|x + 3|))) + 1))) + 3)/(-2(1((-3(2cos(1π(-3|x + 3|))) - 2)/(2(2cos(1π(-3|x + 3|))) + 1))^2 - 3((-3(2cos(1π(-3|x + 3|))) - 2)/(2(2cos(1π(-3|x + 3|))) + 1))) - 3) and g(x) = -3((-1(-3cos(3π((-2x - 2)/(-3x + 4)) - 3) - 1) - 3)/(2(-3cos(3π((-2x - 2)/(-3x + 4)) - 3) - 1) + 1)) + 4 between the vertical lines x = 0.9 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_4_4_325
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(1((-1(5(2|x - 3| - 2) + 1) - 3)/(-2(5(2|x - 3| - 2) + 1) + 1))) + 5, g(x) = -3(2sin(3π(4(3x - 4) - 1) + 3) - 1) - 3, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_326
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(3π(2(3|(3(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) + 1) + 2|) + 3) - 2), g(x) = -3sin(3π(-1(-2(1|x - 1| - 3)^2 - 5(1|x - 1| - 3) - 1)^2 + 4(-2(1|x - 1| - 3)^2 - 5(1|x - 1| - 3) - 1) + 2)) - 3, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_327
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(1(1(-3(2e^(1x) + 1)^2 - 5(2e^(1x) + 1)) + 2) + 2) - 1| + 3, g(x) = 3|(-1(2sin(1π(-5x^2 - 1x)) + 3)) - 3| + 2, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_328
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(1(-2((2(-5x^2 - 4x) - 2)/(-2(-5x^2 - 4x) - 3)) - 2) + 3) + 1 and g(x) = (-3(4(2|(-2sin(1πx + 2) + 1) - 1| + 1)^2 + 4(2|(-2sin(1πx + 2) + 1) - 1| + 1) - 2) + 2)/(1(4(2|(-2sin(1πx + 2) + 1) - 1| + 1)^2 + 4(2|(-2sin(1πx + 2) + 1) - 1| + 1) - 2)) between the vertical lines x = -0.9 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.0
|
math
|
train
|
math_algebra_func_area_level_4_4_329
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(5((1(3e^(-2((1x + 2)/(2x + 3))) + 2) - 2)/(1(3e^(-2((1x + 2)/(2x + 3))) + 2))) + 4) + 3| - 3 and g(x) = -2|(-2|((-3((-3x - 2)/(-2x)) + 3)/(-3((-3x - 2)/(-2x)) + 1)) + 2| + 1) - 2| between the vertical lines x = -0.9 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87.7
|
math
|
train
|
math_algebra_func_area_level_4_4_330
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-2sin(1π(5(2(-4x^2 - 2)^2 - 1(-4x^2 - 2) - 5)^2 - 4)) + 3) + 3)/(-2(-2sin(1π(5(2(-4x^2 - 2)^2 - 1(-4x^2 - 2) - 5)^2 - 4)) + 3) + 3) and g(x) = 2((-1((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))))/(3((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))) - 2))^2 - 1((-1((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))))/(3((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))) - 2)) + 4 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_331
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-1cos(2π((2((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 3)/(-3((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 1)) + 2)) + 1)/(1(-1cos(2π((2((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 3)/(-3((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 1)) + 2)) + 2) and g(x) = -2(3(1|(-2|x + 1| + 3)| - 3) + 5) - 5 from x = 0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_332
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(4(3|((-1(-3|x + 2| + 3) + 3)/(1(-3|x + 2| + 3))) + 1|)^2 - 2(3|((-1(-3|x + 2| + 3) + 3)/(1(-3|x + 2| + 3))) + 1|) + 1)^2 + 1, g(x) = 1|(-5(-2(-2sin(3πx - 2) + 2)^2 - 5(-2sin(3πx - 2) + 2) + 2) + 5) - 1| - 1, x = 3.8, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
64.6
|
math
|
train
|
math_algebra_func_area_level_4_4_333
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(1(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1)^2 + 3(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1) + 4)^2 - 2(1(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1)^2 + 3(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1) + 4) + 4 and g(x) = 1(1|(2((-1x - 3)/(-3x)) + 3) - 3| - 3) + 5 from x = -0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88.7
|
math
|
train
|
math_algebra_func_area_level_4_4_334
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-2(-3|(-3sin(3π((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3)^2 - 2(-3|(-3sin(3π((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3) + 2)^2 - 2(-2(-3|(-3sin(3π((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3)^2 - 2(-3|(-3sin(3π((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3) + 2) and g(x) = (1(2(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)^2 - 4(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)) + 1)/(1(2(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)^2 - 4(2(2|x - 2|)^2 - 3(2|x - 2|) + 3))) from x = 2.3 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.6
|
math
|
train
|
math_algebra_func_area_level_4_4_335
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((2(-1|((2((-1x - 3)/(-1x - 1)) - 2)/(2((-1x - 3)/(-1x - 1)) + 2)) - 1| + 2) - 3)/(-2(-1|((2((-1x - 3)/(-1x - 1)) - 2)/(2((-1x - 3)/(-1x - 1)) + 2)) - 1| + 2) - 1)), g(x) = (2(-3(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2))^2 - 5(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2)) + 2) + 3)/(1(-3(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2))^2 - 5(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2)) + 2) + 2), x = -2.6, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.1
|
math
|
train
|
math_algebra_func_area_level_4_4_336
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(3π(3((-1(-2|(-2x^2 + 3x - 4) + 3| - 3) + 1)/(3(-2|(-2x^2 + 3x - 4) + 3| - 3) - 1)) - 5) + 1) + 1, g(x) = -3e^(2(-3|((3(2|x| - 1) - 1)/(-2(2|x| - 1) - 2)) - 3| + 1)) + 3, x = 0.2, and x = 0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_337
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(3sin(2π(1(-1(2|x + 2|) + 2)^2 + 1(-1(2|x + 2|) + 2) + 1) + 1)))/(2(3sin(2π(1(-1(2|x + 2|) + 2)^2 + 1(-1(2|x + 2|) + 2) + 1) + 1)) - 1), g(x) = 2((-1(-2cos(1π(-2|x + 3|)) - 1) - 2)/(1(-2cos(1π(-2|x + 3|)) - 1))) + 1, x = -4.1, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_338
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-4((-3(-1|(-3|x - 2| + 3) + 1| + 3) - 1)/(-1(-1|(-3|x - 2| + 3) + 1| + 3) + 2)) - 1) - 2)/(2(-4((-3(-1|(-3|x - 2| + 3) + 1| + 3) - 1)/(-1(-1|(-3|x - 2| + 3) + 1| + 3) + 2)) - 1)) and g(x) = 4(-2|(-5(-3sin(1πx - 1)) - 2) + 3| + 1)^2 - 3(-2|(-5(-3sin(1πx - 1)) - 2) + 3| + 1) + 1 between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_4_4_339
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((3((3(-1|(1cos(2πx - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2πx - 2) + 2)| + 1) + 3)) - 2)/(2((3(-1|(1cos(2πx - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2πx - 2) + 2)| + 1) + 3)) - 3))^2 - 5((3((3(-1|(1cos(2πx - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2πx - 2) + 2)| + 1) + 3)) - 2)/(2((3(-1|(1cos(2πx - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2πx - 2) + 2)| + 1) + 3)) - 3)) - 2 and g(x) = -3|((-3((-1((-1x - 1)/(3x + 1)) + 2)/(2((-1x - 1)/(3x + 1)) - 3)) - 2)/(-3((-1((-1x - 1)/(3x + 1)) + 2)/(2((-1x - 1)/(3x + 1)) - 3)) + 4)) + 3| + 1 between the vertical lines x = 1.7 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_340
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|((2(2sin(3π(-2|((3x + 1)/(1x + 2)) - 2| - 3) + 3)) + 3)/(3(2sin(3π(-2|((3x + 1)/(1x + 2)) - 2| - 3) + 3)) - 2)) - 1| - 1 and g(x) = (-3(4(-1(-3e^(2x) - 2) - 5) + 4))/(2(4(-1(-3e^(2x) - 2) - 5) + 4) - 1) between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_341
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-2(3((3(3sin(1πx - 2) - 1) + 1)/(2(3sin(1πx - 2) - 1) - 1)) - 1)^2 + 2(3((3(3sin(1πx - 2) - 1) + 1)/(2(3sin(1πx - 2) - 1) - 1)) - 1) + 2) - 5 and g(x) = -1|(-3(-4(5x^2 + 4x) - 1)^2 + 4(-4(5x^2 + 4x) - 1)) + 1| + 1 from x = -0.4 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_342
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4((-2(-3(-1|(3|x - 2| + 2) - 3|)^2 + 2(-1|(3|x - 2| + 2) - 3|)) + 1)/(-3(-3(-1|(3|x - 2| + 2) - 3|)^2 + 2(-1|(3|x - 2| + 2) - 3|)) - 3)) + 1 and g(x) = -1|(1e^(-1(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4))) - 2) - 2| - 3 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_343
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(1|((2(3e^(2(1x - 3)) - 2) - 2)/(-1(3e^(2(1x - 3)) - 2) + 2)) - 3|) - 1)/(3(1|((2(3e^(2(1x - 3)) - 2) - 2)/(-1(3e^(2(1x - 3)) - 2) + 2)) - 3|)) and g(x) = -1|((2((1(-5x - 3))/(-1(-5x - 3) + 2)) - 3)/(3((1(-5x - 3))/(-1(-5x - 3) + 2)) - 2)) - 1| + 1 between the vertical lines x = -1.0 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_4_4_344
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(3(-1(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) + 1)^2 + 1(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) + 1) + 5) - 3) - 3| + 2 and g(x) = -5(-2((-3(-3sin(3πx + 1) + 3))/(-3(-3sin(3πx + 1) + 3) + 4))^2 + 2((-3(-3sin(3πx + 1) + 3))/(-3(-3sin(3πx + 1) + 3) + 4)) + 3)^2 + 3(-2((-3(-3sin(3πx + 1) + 3))/(-3(-3sin(3πx + 1) + 3) + 4))^2 + 2((-3(-3sin(3πx + 1) + 3))/(-3(-3sin(3πx + 1) + 3) + 4)) + 3) + 5 between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
55.2
|
math
|
train
|
math_algebra_func_area_level_4_4_345
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2(2((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3))^2 + 4((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3)) - 1) + 2) - 1)/(-3(2(2((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3))^2 + 4((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3)) - 1) + 2) + 4) and g(x) = (-3(4(-2sin(2π(3|x + 2| - 3) - 2)) - 2) - 2)/(-2(4(-2sin(2π(3|x + 2| - 3) - 2)) - 2) + 3) from x = 3.0 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_346
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-2(-3((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2))^2 + 2((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2)) + 1)^2 - 2(-3((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2))^2 + 2((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2)) + 1) - 1) - 3, g(x) = 1|((-2(-2(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 5) - 2)/(-1(-2(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 5) + 3)) + 2| - 3, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_4_4_347
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-2e^(-1(2(-5((-2x + 2)/(-2x - 1)) - 2)^2 - 5(-5((-2x + 2)/(-2x - 1)) - 2) - 1)) - 2) + 5 and g(x) = 5(2|(-4(-1e^(1x) + 2)^2 - 3(-1e^(1x) + 2))| + 1) - 5 from x = 0.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
33.4
|
math
|
train
|
math_algebra_func_area_level_4_4_348
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-2|(5((-3(-3x))/(2(-3x) + 2)) + 3)| + 2) - 2 and g(x) = (1((2(3|(-3|x - 3| - 1) - 1| + 1) + 1)/(-1(3|(-3|x - 3| - 1) - 1| + 1) - 2)) + 1)/(-1((2(3|(-3|x - 3| - 1) - 1| + 1) + 1)/(-1(3|(-3|x - 3| - 1) - 1| + 1) - 2)) + 2) between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_349
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(1(-1sin(2π(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3)^2 - 2(-1sin(2π(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3) + 5)^2 - 1(1(-1sin(2π(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3)^2 - 2(-1sin(2π(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3) + 5) - 2 and g(x) = 1(4(-3|((1x - 1)/(1x)) + 2| + 1))^2 + 1(4(-3|((1x - 1)/(1x)) + 2| + 1)) between the vertical lines x = 0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.9
|
math
|
train
|
math_algebra_func_area_level_4_4_350
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2e^(-2(1|(-3|(-4(-5x^2 - 4x + 4)^2 - 5(-5x^2 - 4x + 4) + 4) + 1| + 1)|)) + 2, g(x) = 1|(-2(3((1x - 1)/(3x))^2 + 4((1x - 1)/(3x)) + 5) + 5) - 1| - 1, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_351
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(2|(-1|(2(4x - 2)^2 - 4(4x - 2) + 1) - 3| + 2) - 2| - 1) + 3 and g(x) = -1(4(1(3sin(1πx + 2) - 1) + 1) - 1) + 2 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_352
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(1e^(-1(2|(-3|(-3x^2 + 3x + 4) - 2| - 1) + 1| - 3)))^2 - 1(1e^(-1(2|(-3|(-3x^2 + 3x + 4) - 2| - 1) + 1| - 3))) + 2, g(x) = (3(-5(-1(1|x + 2| + 3)) + 4))/(1(-5(-1(1|x + 2| + 3)) + 4)), x = 1.4, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
33.6
|
math
|
train
|
math_algebra_func_area_level_4_4_353
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(1(-4(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5)^2 + 2(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5) + 2) + 1) + 2)/(1(1(-4(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5)^2 + 2(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5) + 2) + 1) + 1), g(x) = 1(-3cos(3π((3(-3x + 1) + 2)/(-2(-3x + 1) + 3)) - 2) - 3) + 4, x = 1.0, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.6
|
math
|
train
|
math_algebra_func_area_level_4_4_354
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((-3(2((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1))^2 - 4((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1)) - 1) + 3)/(3(2((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1))^2 - 4((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1)) - 1) + 1)) + 2| - 1, g(x) = (3((-3(-5(4x) + 1) + 1)/(2(-5(4x) + 1) + 3)) + 2)/(-1((-3(-5(4x) + 1) + 1)/(2(-5(4x) + 1) + 3)) + 3), x = 3.2, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.3
|
math
|
train
|
math_algebra_func_area_level_4_4_355
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-3(-4(1(3sin(1πx - 3) + 1)^2 + 4(3sin(1πx - 3) + 1) + 1) + 2) - 4) + 3)/(-3(-3(-4(1(3sin(1πx - 3) + 1)^2 + 4(3sin(1πx - 3) + 1) + 1) + 2) - 4) - 1) and g(x) = 1(3(-3sin(1π(-1|x + 2| + 3) + 2) - 3)^2 - 1(-3sin(1π(-1|x + 2| + 3) + 2) - 3)) - 5 between the vertical lines x = -1.6 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
78.7
|
math
|
train
|
math_algebra_func_area_level_4_4_356
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(3(-1((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3))^2 + 3((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3)) + 3)^2 - 3(-1((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3))^2 + 3((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3)) + 3) - 2) - 3|, g(x) = 1|(2(-2cos(2π(-3x^2 + 5x) - 3) - 3)^2 + 3(-2cos(2π(-3x^2 + 5x) - 3) - 3) + 5) - 3| - 2, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_4_4_357
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-2|(3(2|(-1x + 3) - 1| - 2) + 2) + 3| - 1)^2 + 1(-2|(3(2|(-1x + 3) - 1| - 2) + 2) + 3| - 1) + 2, g(x) = 2|(-1|(3(3x - 3)^2 + 3(3x - 3) + 2) + 1| + 2) - 3| + 1, x = 1.6, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
110.5
|
math
|
train
|
math_algebra_func_area_level_4_4_358
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-3|(2(-5(-3x - 4)^2 + 1(-3x - 4) - 2)^2 + 3(-5(-3x - 4)^2 + 1(-3x - 4) - 2) + 5)| + 3) - 3)/(-1(-3|(2(-5(-3x - 4)^2 + 1(-3x - 4) - 2)^2 + 3(-5(-3x - 4)^2 + 1(-3x - 4) - 2) + 5)| + 3) + 2) and g(x) = (1(-1|(2cos(2π(-3|x - 2|) + 1) - 1) - 2| + 3) + 3)/(2(-1|(2cos(2π(-3|x - 2|) + 1) - 1) - 2| + 3) + 2) between the vertical lines x = -1.2 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_4_4_359
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(2(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1)^2 - 3(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1) - 2) + 1)/(1(2(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1)^2 - 3(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1) - 2) - 3), g(x) = 1|((1(-3|((3x - 3)/(-3x - 3)) + 3| - 2) - 3)/(-1(-3|((3x - 3)/(-3x - 3)) + 3| - 2) - 1)) + 3| - 1, x = -1.8, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_360
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(1(-5(1cos(3π(3|x + 3| - 1) - 3) - 3) + 3) - 4)| + 3 and g(x) = 2(1|(3|(-1x + 5) - 2| + 1) + 3| - 1)^2 - 2(1|(3|(-1x + 5) - 2| + 1) + 3| - 1) + 3 from x = 2.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_361
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((-3(1(4(2|x + 2| - 3) + 5) - 4) + 3)/(-2(1(4(2|x + 2| - 3) + 5) - 4) + 3))^2 + 2((-3(1(4(2|x + 2| - 3) + 5) - 4) + 3)/(-2(1(4(2|x + 2| - 3) + 5) - 4) + 3)) - 3 and g(x) = -2|(4(1(-5x^2 + 3) + 4) + 2) + 1| - 1 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_4_4_362
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(5(-3|(3|(1e^(-1x) - 2)|) + 3| - 3)^2 - 1) + 1)/(-3(5(-3|(3|(1e^(-1x) - 2)|) + 3| - 3)^2 - 1) + 4) and g(x) = (2((2((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 1)/(3((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 2)) + 1)/(-2((2((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 1)/(3((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 2)) - 3) between the vertical lines x = 1.2 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_363
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(1|(-5(3e^(1(-2|x| + 3)) + 1) + 2) + 3| - 1) + 3 and g(x) = (2(-1(-2sin(2π(-3x^2 + 4x - 4) + 1))^2 + 3(-2sin(2π(-3x^2 + 4x - 4) + 1)) - 5) - 1)/(3(-1(-2sin(2π(-3x^2 + 4x - 4) + 1))^2 + 3(-2sin(2π(-3x^2 + 4x - 4) + 1)) - 5) + 3) from x = -2.5 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_364
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π((1(2|(-2|(-1|x| + 3)| - 3) - 3| + 2) + 2)/(-3(2|(-2|(-1|x| + 3)| - 3) - 3| + 2) - 2)) - 2) + 2 and g(x) = 5(-1(2(-3x - 2) + 2)^2 + 4) + 4 between the vertical lines x = -0.7 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.9
|
math
|
train
|
math_algebra_func_area_level_4_4_365
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((-3((3(-1|(1e^(1x) - 3) - 2| + 1) - 3)/(-2(-1|(1e^(1x) - 3) - 2| + 1) + 3)) + 2)/(3((3(-1|(1e^(1x) - 3) - 2| + 1) - 3)/(-2(-1|(1e^(1x) - 3) - 2| + 1) + 3)) + 3)) + 3| - 3 and g(x) = 2(5(-2|(-5x^2 + 2x + 3) - 3| + 1)^2 + 5(-2|(-5x^2 + 2x + 3) - 3| + 1) - 1) + 3 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_366
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(1|(-5((2(-1sin(2πx + 3) - 1) - 1)/(2(-1sin(2πx + 3) - 1) + 2))^2 - 1((2(-1sin(2πx + 3) - 1) - 1)/(2(-1sin(2πx + 3) - 1) + 2)) - 1) + 2|) - 1| - 3 and g(x) = 3sin(2π((1(-2(5x^2 + 1x - 1)^2 - 4(5x^2 + 1x - 1) + 1) + 2)/(1(-2(5x^2 + 1x - 1)^2 - 4(5x^2 + 1x - 1) + 1) + 1)) - 1) - 1 between the vertical lines x = -4.6 and x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.0
|
math
|
train
|
math_algebra_func_area_level_4_4_367
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(1π(2|((1(3|(1x^2 + 3x - 3) + 3| - 1) + 3)/(-3(3|(1x^2 + 3x - 3) + 3| - 1) + 4)) + 3| + 1) - 1) - 1, g(x) = 1(3(-2|(2|x - 1|) - 1| + 3)^2 - 3(-2|(2|x - 1|) - 1| + 3) - 1) - 2, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_368
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-1(-3sin(1π(4(4x^2 - 2x + 2)^2 + 2(4x^2 - 2x + 2) + 4)) - 3)^2) + 1| + 1 and g(x) = (-1(5(2|(2|x - 3| - 3) + 2| - 2) + 4) + 3)/(2(5(2|(2|x - 3| - 3) + 2| - 2) + 4) - 3) from x = 2.1 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.7
|
math
|
train
|
math_algebra_func_area_level_4_4_369
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3((-1(1(1sin(1πx + 3) - 1) + 4) + 3)/(-1(1(1sin(1πx + 3) - 1) + 4))) - 4) - 2)/(-1(-3((-1(1(1sin(1πx + 3) - 1) + 4) + 3)/(-1(1(1sin(1πx + 3) - 1) + 4))) - 4) + 3) and g(x) = (-3((-1(-1|(3x + 4) - 3| - 3) + 3)/(2(-1|(3x + 4) - 3| - 3) + 1)) - 3)/(1((-1(-1|(3x + 4) - 3| - 3) + 3)/(2(-1|(3x + 4) - 3| - 3) + 1))) from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_370
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4((1(-3(-2(1x + 1) - 1) - 5) - 2)/(-1(-3(-2(1x + 1) - 1) - 5) + 2)) - 3 and g(x) = -5(-1(-3(1|x| - 1) + 1) - 1) - 1 between the vertical lines x = -1.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35.2
|
math
|
train
|
math_algebra_func_area_level_4_4_371
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-2|(1(1(-1x^2 + 2x) - 3) + 2) + 3| + 2)| + 2 and g(x) = 5((-1(-5(2|x + 1| - 3) - 5) + 2)/(3(-5(2|x + 1| - 3) - 5) + 3)) + 1 from x = 2.8 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_372
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(3cos(3π(-4(-3|((-3x + 3)/(-3x - 2)) - 2| + 1)^2 + 1(-3|((-3x + 3)/(-3x - 2)) - 2| + 1) + 2) + 1) - 2) - 2 and g(x) = (-3((2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) + 1)/(2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) - 1)) + 3)/(3((2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) + 1)/(2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) - 1))) from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_373
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-1(-1cos(1π((1(3|x + 3| + 2) - 2)/(-3(3|x + 3| + 2) - 2))) + 2)^2 + 1(-1cos(1π((1(3|x + 3| + 2) - 2)/(-3(3|x + 3| + 2) - 2))) + 2) + 3) - 4, g(x) = 3sin(2π(3(-4(3|x - 3| + 2)^2 - 1)^2 + 3(-4(3|x - 3| + 2)^2 - 1) - 5) - 3) - 3, x = 2.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_374
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3|(5((-2(-2|x| + 2) - 3)/(-2(-2|x| + 2) + 1)) - 1) - 1|))/(1(3|(5((-2(-2|x| + 2) - 3)/(-2(-2|x| + 2) + 1)) - 1) - 1|) - 3) and g(x) = 4(-3(-1sin(3π(-1x^2 - 4) - 2) + 3) - 3) - 2 from x = -3.3 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
75.5
|
math
|
train
|
math_algebra_func_area_level_4_4_375
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-2(1|((1(-2x + 4) + 3)/(-3(-2x + 4) - 3)) + 3|))^2 - 4(-2(1|((1(-2x + 4) + 3)/(-3(-2x + 4) - 3)) + 3|)) - 1 and g(x) = 1(-1e^(1(5(-3x - 1)^2 - 4(-3x - 1) + 2)) - 3) + 3 between the vertical lines x = -0.7 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.1
|
math
|
train
|
math_algebra_func_area_level_4_4_376
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|((2(-2(-1|(3x) + 3| - 2)^2 + 5(-1|(3x) + 3| - 2) - 2) - 1)/(2(-2(-1|(3x) + 3| - 2)^2 + 5(-1|(3x) + 3| - 2) - 2) + 3)) + 2| + 1 and g(x) = 5(4(-4((2x + 3)/(-1x + 2))^2 + 2((2x + 3)/(-1x + 2)) + 5) - 4) between the vertical lines x = -4.0 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
215.8
|
math
|
train
|
math_algebra_func_area_level_4_4_377
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(4(-1cos(1π((2(3|x + 2| + 3) - 3)/(-3(3|x + 2| + 3))) - 2) - 3) + 3) + 1| + 2, g(x) = 2|(3(4(1x) - 1) - 4) - 1| - 2, x = 0.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.8
|
math
|
train
|
math_algebra_func_area_level_4_4_378
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3((-2(4(-1(1sin(1πx) - 1) + 5)^2 - 4(-1(1sin(1πx) - 1) + 5)) + 3)/(-2(4(-1(1sin(1πx) - 1) + 5)^2 - 4(-1(1sin(1πx) - 1) + 5)) + 3)) + 1)/(2((-2(4(-1(1sin(1πx) - 1) + 5)^2 - 4(-1(1sin(1πx) - 1) + 5)) + 3)/(-2(4(-1(1sin(1πx) - 1) + 5)^2 - 4(-1(1sin(1πx) - 1) + 5)) + 3)) - 3), g(x) = 3(-1sin(1π(-4(-3x - 2)) - 1) - 2)^2 - 1(-1sin(1π(-4(-3x - 2)) - 1) - 2) - 5, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_379
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(3π((-2(-1|(-1x - 4)| - 2) - 2)/(-1(-1|(-1x - 4)| - 2) - 2)) + 3) + 3)^2 - 5(2cos(3π((-2(-1|(-1x - 4)| - 2) - 2)/(-1(-1|(-1x - 4)| - 2) - 2)) + 3) + 3) - 2 and g(x) = 3sin(2π(3|(4((-2x + 3)/(3x + 1))^2 + 5((-2x + 3)/(3x + 1)) + 4) + 2| - 1) + 2) between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_380
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2((-1(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) + 1)/(3(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) - 2))^2 - 4((-1(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) + 1)/(3(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) - 2)) - 5, g(x) = -5(2|(4(1x) - 1) - 3| - 3) - 2, x = 0.6, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.1
|
math
|
train
|
math_algebra_func_area_level_4_4_381
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(1|(-2|(2|(-1x^2 - 2x + 3) - 2| - 3) - 3| - 2) - 1| - 3) - 1| - 2 and g(x) = 1(1|((-3(1|x| - 2) - 1)/(-1(1|x| - 2) - 3)) + 1| - 1)^2 + 3(1|((-3(1|x| - 2) - 1)/(-1(1|x| - 2) - 3)) + 1| - 1) - 4 between the vertical lines x = -0.2 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_382
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3cos(2π(2|(-2|(-1|(1x^2 - 2x + 3) - 3|) + 2| - 3)| + 2) - 2) and g(x) = -5(-1|(2|(1x^2 - 2) + 1| - 1) - 3| + 3)^2 + 2(-1|(2|(1x^2 - 2) + 1| - 1) - 3| + 3) + 3 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_383
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(1((-1(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)/(2(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1))^2 - 4((-1(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)/(2(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)) + 3) - 3| + 3 and g(x) = -1|(-3(-3((3x + 3)/(-1x + 2))^2 + 1((3x + 3)/(-1x + 2)) + 3)^2 + 5(-3((3x + 3)/(-1x + 2))^2 + 1((3x + 3)/(-1x + 2)) + 3) + 4) + 3| + 1 from x = -2.5 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_384
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(1|(-1(1|(2x^2 + 2x + 2) + 1| + 3) + 4) - 3| + 1) - 3)/(-1(1|(-1(1|(2x^2 + 2x + 2) + 1| + 3) + 4) - 3| + 1)) and g(x) = (-1(-1(3((-3x)/(1x + 1))^2 - 3((-3x)/(1x + 1)) + 1) + 3) + 2)/(2(-1(3((-3x)/(1x + 1))^2 - 3((-3x)/(1x + 1)) + 1) + 3)) from x = -0.3 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_4_4_385
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-2(-3sin(3π((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1)^2 - 4(-3sin(3π((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1) + 5) - 2)/(-2(-2(-3sin(3π((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1)^2 - 4(-3sin(3π((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1) + 5) - 1) and g(x) = 4(-3(3(-2e^(2x) + 1)^2 - 1(-2e^(2x) + 1) - 1)^2 + 2(3(-2e^(2x) + 1)^2 - 1(-2e^(2x) + 1) - 1) + 3) between the vertical lines x = -3.0 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.5
|
math
|
train
|
math_algebra_func_area_level_4_4_386
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-3sin(2π((2(-2x - 5) + 3)/(1(-2x - 5))) + 1) - 2) + 2) - 3)/(-2(-2(-3sin(2π((2(-2x - 5) + 3)/(1(-2x - 5))) + 1) - 2) + 2) + 1) and g(x) = 2|(2|(-3|((2x - 1)/(1x)) - 3| - 2) - 2|) + 1| + 1 between the vertical lines x = -1.9 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.4
|
math
|
train
|
math_algebra_func_area_level_4_4_387
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 3)/(2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 2))^2 + 1((2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 3)/(2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 2)) - 1 and g(x) = (-2(2(1e^(-1(5x + 4)))^2 - 5(1e^(-1(5x + 4))) - 4) - 1)/(1(2(1e^(-1(5x + 4)))^2 - 5(1e^(-1(5x + 4))) - 4) - 2) from x = 0.7 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_388
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(1|((3(-2sin(1π(-3|x + 2| + 3) - 3) + 1) - 1)/(1(-2sin(1π(-3|x + 2| + 3) - 3) + 1) + 3)) + 3| - 1)^2 - 3(1|((3(-2sin(1π(-3|x + 2| + 3) - 3) + 1) - 1)/(1(-2sin(1π(-3|x + 2| + 3) - 3) + 1) + 3)) + 3| - 1) - 1, g(x) = 4(-1|(2cos(1π((-3x + 1)/(1x + 3)) + 3) - 1)| + 2)^2 - 5(-1|(2cos(1π((-3x + 1)/(1x + 3)) + 3) - 1)| + 2) - 2, x = -4.5, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.9
|
math
|
train
|
math_algebra_func_area_level_4_4_389
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(2(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2)^2 - 5(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2) + 2)^2 + 1(2(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2)^2 - 5(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2) + 2) - 5 and g(x) = -3|(-1(3cos(2π(-1x^2 - 2x - 2) - 3) - 3) + 4) - 2| + 3 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_390
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(2(-2|(3|((-3x + 2)/(2x + 2)) - 3|) - 1| + 2) + 1)^2 - 4(2(-2|(3|((-3x + 2)/(2x + 2)) - 3|) - 1| + 2) + 1), g(x) = (2(-1((2(1x^2 + 3) - 3)/(1(1x^2 + 3) - 2)) + 3))/(-1(-1((2(1x^2 + 3) - 3)/(1(1x^2 + 3) - 2)) + 3) - 3), x = -0.5, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_4_4_391
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|((-2(-2|(-1(-3x^2 + 2x) - 1) + 2| - 3) + 2)/(2(-2|(-1(-3x^2 + 2x) - 1) + 2| - 3) + 1)) - 2| - 3, g(x) = -1|(-3|((2(3|x - 2| - 2) + 1)/(1(3|x - 2| - 2) - 3))| + 3) + 1|, x = 0.8, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.5
|
math
|
train
|
math_algebra_func_area_level_4_4_392
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(3sin(1π(3|(3(-5x^2 - 2x - 4)^2 - 2(-5x^2 - 2x - 4) + 4) + 2| - 2) - 3) - 3) - 3| + 3 and g(x) = -1|(2(1(-1x^2 + 3x + 3) + 3)) + 2| + 2 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_393
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(3|((1(-5(-1x^2 - 5x - 2) + 5) - 1)/(3(-5(-1x^2 - 5x - 2) + 5) + 1)) - 1| + 3) - 3)/(2(3|((1(-5(-1x^2 - 5x - 2) + 5) - 1)/(3(-5(-1x^2 - 5x - 2) + 5) + 1)) - 1| + 3) - 1), g(x) = 3|((2((-1(-2sin(2πx - 3)) - 1)/(-3(-2sin(2πx - 3)) + 4)) + 1)/(-2((-1(-2sin(2πx - 3)) - 1)/(-3(-2sin(2πx - 3)) + 4)) + 3)) + 2| - 2, x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_4_4_394
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-3e^(-1(-2((-1(1|x - 1| - 2) + 3)/(2(1|x - 1| - 2) - 1)) + 4)) + 1) - 5 and g(x) = -3cos(2π(1(1|(-2|x| - 1) + 2| + 1)^2 + 2(1|(-2|x| - 1) + 2| + 1) + 5) + 3) - 2 between the vertical lines x = -4.5 and x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_395
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((-1(-3cos(3π(-1(5x + 5) - 5) - 1) + 3) - 2)/(1(-3cos(3π(-1(5x + 5) - 5) - 1) + 3) - 2)) + 1| - 1 and g(x) = (-2((-3(2sin(3π(-1|x + 2| - 2) - 3) + 2))/(2(2sin(3π(-1|x + 2| - 2) - 3) + 2) - 1)))/(-1((-3(2sin(3π(-1|x + 2| - 2) - 3) + 2))/(2(2sin(3π(-1|x + 2| - 2) - 3) + 2) - 1)) - 1) from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_4_4_396
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((3(1|((-2((-1x + 3)/(-1x - 2)) + 2)/(-1((-1x + 3)/(-1x - 2)) + 3)) - 2| + 3) + 2)/(1(1|((-2((-1x + 3)/(-1x - 2)) + 2)/(-1((-1x + 3)/(-1x - 2)) + 3)) - 2| + 3) + 3))^2 - 1 and g(x) = (-3(-1(2(2x) - 2)^2 + 3(2(2x) - 2)) + 3)/(2(-1(2(2x) - 2)^2 + 3(2(2x) - 2)) + 3) from x = 0.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.7
|
math
|
train
|
math_algebra_func_area_level_4_4_397
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((-1((-2((-1(2sin(2πx) + 1) + 2)/(1(2sin(2πx) + 1) - 2)) + 2)/(1((-1(2sin(2πx) + 1) + 2)/(1(2sin(2πx) + 1) - 2)) + 2)) - 2)/(1((-2((-1(2sin(2πx) + 1) + 2)/(1(2sin(2πx) + 1) - 2)) + 2)/(1((-1(2sin(2πx) + 1) + 2)/(1(2sin(2πx) + 1) - 2)) + 2)))) - 3, g(x) = -1|(-3(3|(-1x) - 2|) + 4)|, x = -3.3, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.1
|
math
|
train
|
math_algebra_func_area_level_4_4_398
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(2e^(2(-3((-1(4x - 2))/(-2(4x - 2) + 3))^2 + 5((-1(4x - 2))/(-2(4x - 2) + 3)) - 2)) + 3) - 2| + 1 and g(x) = -5(3sin(2π(-4(-3|x| - 2) + 3) - 2) - 3)^2 + 5(3sin(2π(-4(-3|x| - 2) + 3) - 2) - 3) - 3 between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.9
|
math
|
train
|
math_algebra_func_area_level_4_4_399
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-5(2cos(1π(3|(-2x^2 + 1x + 5) - 2| - 2) - 1) + 3) + 4) - 2)/(-3(-5(2cos(1π(3|(-2x^2 + 1x + 5) - 2| - 2) - 1) + 3) + 4) - 2), g(x) = -2|(-5(1(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) - 3) - 4) - 1| - 1, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
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