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Question: volume integral of torus in spherical coordinates seems to have a glitch?

Question:volume integral of torus in spherical coordinates seems to have a glitch?

Robert Jantzen 65 Maple
integration multivariate
April 13 2020
2

This is an interesting exercise in setting up triple integrals in cylindrical and spherical coordinates to obtain a formula that is immediate without any calculation using the theorem of Pappus. The cylindrical integral is easy. The spherical one is hard, but Maple gives me the result off by a factor of minus one half for generic values of the two radii, but the correct result for concrete numbers! I cannot figure out what I am doing wrong. Any ideas?
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2500/handouts/torusvolume.mw
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