"fred" wrote...
....
Why shouldn't a language calculate equations in the way a calculus teacher
would? ... Apparently they just don't. I'm guessing it's because
the programmers don't know the right way to do it, because most programmers
aren't mathematicians; or because there would be too much work involved at
any given point in the project. Why else?
....

Maybe because computers aren't usually working with equations or true real
(or complex) numbers. Computers generally deal with finite precision binary
arithmetic calculations, and those have complications that have ensnared
many mathematicians who don't appreciate the difference.

For instance, binary floating point addition and multiplication are both
commutative, as expected, but neither is strictly associative, only
approximately so. Evaluation order using the same operator is critical in
software development and usually not at all in mathematics.