Revision history [back]

you can certainly compare the numeric outputs for constants: in maxima you do

 assume(H>0);
 integrate(1,z,sqrt(x^2+y^2),H+sqrt(3)*y/3);
 integrate(%,y,-sqrt(H^2*(3-sqrt(3))^2/4-x^2),sqrt(H^2*(3-sqrt(3))^2/4-x^2));
 r:integrate(%,x,-H*(3-sqrt(3))/2,H*(3-sqrt(3))/2);
 expand(ev(subst([H=1],r),numer));

and you get 0.729009112317963 - 13.831305954985441e-9 %i, while the Mathematica's constant term is

 ev(-(-3+sqrt(3))*%pi/4,numer);

is 0.9958449670166816. So it's really different answers, and probably Maxima is wrong, as the imaginary term looks suspiciously large.

The only way to find out for sure is to compute this by some other means...