I found this interesting issue (bug?) in the well known Wolfram Mathematica ® system.
When you have something like sqrt(x)^2 (where sqrt means the square root, and ^ an exponentiation), what would you expect it to be in a graphic? Well, some might say it's the graphic of x, but that would be wrong. Although the square root may be associated with the power by two as its inverse function, that's only true for the non-negative side of the x axis. There's no inverse of x^2, the result is not a function, so you can't simply cancel the functions and return x.
So, the graphic of this would only be x on the positive side of the x axis, on the negative side the graphic is as possible as the square root of a negative number (mnham, mnham, complexes...), which is impossible if we're in the plane that we're supposed to, the real plane.
Now, here's the Mathematica's graphic of that:
So, or Mathematica simplified the sqrt(x)^2 in x^(1/2)^2, canceled the exponents and returned x, or it simply processed the square root of negative numbers as complexes, which, of course, squared, returns x, but that's not a valid operation in the real plane.
I find it interesting how respectful systems have bugs like these.