  In this paper, we present a uniform formula for the integration of
polynomials over the unitary, orthogonal, and symplectic groups using
Weingarten calculus. From this description, we further simplify the integration
formulas and give several optimizations for various cases. We implemented the
optimized Weingarten calculus in Maple in a package called IntHaar for all
three compact groups. Here we will discuss its functions, provide instructions
for the package, and produce some examples of computed integrals.
