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?