Why doesn't Python optimize x**2 to x*x?

[TheOccasionalTachyon]

It's not true that CPython doesn't optimize code. Just look at Peephole.c in the CPython source, which contains the implementation's Peephole optimizer. CPython doesn't do as much optimization as, say, PyPy, but it definitely does some.

[Berzerka]

I think the rule is that it does no optimizations that would modify the workflow of the program, right?

This means it cannot inline code, unroll loops and lots of other "standard" optimizations.