Guess what?! Excel IS NOT MATHEMATICAL SOFTWARE like Maple, Mathematica,
MathCAD, MatLab, etc. It's a SPREADSHEET! It's meant for secretaries and
bean counters, and if others (mis)use it as mathematical software, THEY
HAVE
NO ONE BUT THEMSELVES TO BLAIM WHEN IT DOESN'T WORK AS 'EXPECTED'.

(Blame, not blaim)
If there isn't "math" to base it on, what is there?

However, having done software development myself, I think it most likely
that it's just a bug and just hasn't been fixed yet. In fact, to me,
putting in a zero and getting a different answer proves it's wrong.

No. Putting a zero in front of it converts the unary/monadic negation
operator into a diadic suntraction operator. It's parsed FUNDAMENTALLY
DIFFERENTLY. Even if unary minus had lower priority than exponentiation,
it'd still be parsed differently. Maybe you think you've done software
development, but you don't seem to know much about language design or
parsing.

"Maybe you think you've done software development" ... okay, whatever,
that's kind of unjustifiably condescending, but
I'm not sure what your point is. I haven't done language design. no.
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?

Given the fun discussions that infrequently occur with regard to different
decimal points and digit groupings in non-English speaking and
non-European
countries, are you sure all math texts in all languages adopt the exact
same
operator precedence?

I guess that any formula in any physics journal
is univerally calculable. Yes.
If you have to pick a software and then
look up its idiosyncracies instead of assuming it
follows math convention, then I suppose you are right.
Is this right? I say 'no'. Is it common? I guess it is relativly so.