I posed an integration problem and Maple solved it so easily I decided I would like to get Maple.  I'm waiting to hear whether Maplesoft will sell me the student version.  While I'm waiting, I would like to ask this group a question I've always had about systems like Maple.  I will start by posing a problem:

Let C be a unit circle and let P be a point on C.  Draw a bigger circle B with P as center which crosses C at two diametrically opposed points of C.  What is the area of the crescent-shaped region inside C and outside B?

This problem has a simple answer, but whether the solution is simple depends on the solution method chosen.  I can solve the problem in my head without even a pocket calculator if I choose the right solution method.

Now here is my real question.  Is there a "neutral" way to pose this problem to Maple?  By that I mean to pose it as I have to you, without presupposing a particular solution method.  Or, would that make Maple a different kind of system from what it is, and if so, what do you call that kind of system?

Thanks,

Bob Baker