So we have :
(1/3)*sig0*h^3*(int(int(sin((1/3)*arctan(y, x)), x = 0 .. r), y = 0 .. 2*Pi))
Is it possible to optimise it? (in maple or any other way...)
How I got here:
> R := 1;
H := h;
sigma[0] := sig0;
sigma := sigma[0]*z^2*sin((1/3)*`ϕ`);
toCar := eval(sigma, {r = sqrt(x^2+y^2), z = z, `ϕ` = arctan(y, x)});
> Q := int(int(int(toCar, x = 0 .. r), y = 0 .. 2*Pi), z = 0 .. H);