Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:4/4
K:F
['A F2 FA cAAc (A/B/c) (FA) cAAf', 'fc d3 f']  
X:1
L:1/8
M:4/4
K:F
 A | F2 FA cAAc | (A/B/c) (FA) cAAf | F2 (FA) cAAc | dfc>A G/G/G G :| g | (f/g/a) fc d3 f | 
 cfAf cfAf | (a/g/f/e/) fc d3 f | cAfd cAGg | (f/g/a) fc d3 f | cfAf cfAf | (a/g/f/e/) fc d>efd | 
 cAfd cAFA ||  