There is a problem that "very well done math" isn't necessarily cheap. Some equations are confidential and or under patent. Some things involve long libraries of computer programming that aren't very readable. If you already knew the method you'd know what it's doing: on the other hand the computer code isn't in a presentable form.

(equations you can learn from free books, after all)

I'm trying to tell you I'm a Mathematica fan, it is a great environment, and that finding an environment which "posts al lthe math it's doing when asked" is not necessarily what you should most look for. We all wish for that but it's not presently what you should most wish for.

Dear John,

do you mean something like this?

Within Mathematica this might work:

{WolframAlpha[
  "integrate sin(x)cos(x)^2", {{"IndefiniteIntegral", 1}, "Content"}, 
  PodStates -> {"IndefiniteIntegral__Step-by-step solution"}], 
 WolframAlpha[
  "integrate sin(x)cos(x)^2", {{"IndefiniteIntegral", 2}, "Content"}, 
  PodStates -> {"IndefiniteIntegral__Step-by-step solution"}]}

Best wishes, Marco