From: //noreply@axelvogt.de   
      
   Do not mind, Maple has a bug:   
      
   expr:= log(1 + 2*a*cos(2*x) + a^2)*sin(x)^2:   
   R:=Int(expr,x=0..Pi/2);        # task   
   r:= value(%) assuming 1 < a^2; # result   
      
   Now check:   
      
   R=r; eval(%, a=3/2);   
   evalf(%);                      # using 15 decimals   
                                                                  -13   
      0.113304326861497 = -1.17809724509622 - 0.180900313639568 10    I   
      
   Ignoring the spurious imaginary it has false sign, at least.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)