Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:F
['', '(3c=B_B AFCF Acfe gfdB', '(3cB_B AD^FA c_edc cBBA B2 BA GB^ce']  
X:1
L:1/8
M:4/4
K:F
 (3c=B_B |: AFCF Acfe | gfdB D2 GF | EB,CE GBdc | BAAB G2 (3c=B_B | AFCF Acfe | gfdB bagf | 
 ec=Bc _BGEG |1 (3FEF AG F2 (3c=B_B :|2 (3FEF AG F2 EF |: GEB,C EGBd | dcc=B c2 (3cB_B | 
 AD^FA c_edc | cBBA B2 BA | GB^ce gbab | F_A=Bd f^fg^g | afcA BGEG | (3FEF AG F2 ED :|  