LOL!
keltuzar, you dont integrate with the Maya API! What you should do is study the problem carefully, write out the math AND/BUT make sure you're solving the general problem instead of a very narrow one (else your math will fail). The Maya API is for doing the Maya specific stuff, and that does not include integrating. Anyway, I suspect whatever integration you have to do will be analytical (and not numerical), and so you can do the math on paper and code the final formula in C++.
Caveat: Make sure you're using the right math, else you'll get horribly inaccurate answers. All I said was that geodesics are worth looking into and might well be the way to go, but its up to you to be sure that geodesics indeed solve your problem.
You'll have little problem understanding all this if you've written a few programs before.
PS:
I hope you're dealing with a single surface and not a patch or trim surface because they are a lot trickier to deal with.
