I have been working on an implementation of my problem in three dimensions. Generally, it is hard to generalize from one to two dimensions, and it is even harder to go up to three. This case is no exception.
When you want to integrate a function of more than two dimensions, the best way to do it is called Monte Carlo integration, a method in which you select random points in space, evaluate the function there, and sum them all up to get an idea of the integral. How to select those random points in space is a difficult problem. And the optimal method for one problem isn't necessarily optimal for another problem.
Today I've been trying to figure out how to meld one person's Monte Carlo program with another person's random number generator. So far, so bad. But I may be able to figure out a hack which might work. I may need the help of my expert office-mates, but eventually, I will figure this out.