So, is -x^2^ a positive, negative, or undefined quantity for real-valued
x? Ask any physicist or mathematician and they will say that it is a
negative number for real valued x making things like: exp(-x^2^) between
0 and 1. That is why it came as a **BIG** surprise to me that computer
scientists don't think that, and a program like Excel will interpret:

=-5\^2

as ** positive** 25! After taking quite a while debugging a student
problem calculating the normal distribution in Excel, it got me on a
quest (and an argument with a colleague) to figure out who else thought
this way. I checked Matlab, Mathematica, Python, and Google as well as
a calculator on the computer. All interpreted -5\^2 (properly) as -25.
To do otherwise, I believe, is perverse for any application that is
doing mathematical applications. I was directed to this page, which
outlines many languages. Pretty much just Excel, COBOL, Chipmunk BASIC
and a few small scripting languages take the "unary minus" approach,
which makes "unary minus" have precedence over exponentiation.

I am not sure why anyone would consider this a good idea, for working with actual math equations. Of course one could add parentheses, but which is clearer:

y=exp(-x\^2)

or

y=exp(-(x\^2))

The second is obviously not ambiguous, but less clear. Anyway, that is the entire reason why we have order of operations, so we don't have to do:

5+(3*4)-(2*3)+(2*(3\^3))

So, Excel, come into at least the 20th century and figure out that exponentiation trumps "minus", whatever you want to call it.