The powmod function computes $a^n\mathbf{mod}b$ where a and b are polynomials in x and n is an integer, possibly negative.  The case of n positive could also be computed as $\mathrm{rem}\left(a^n\,b\,x\right)$ but powmod is more efficient and uses the method of binary powering with remainder.

$\mathrm{powmod}\left(x+1\,16\,x^2+1\,x\right)$

$256$

$\mathrm{powmod}\left(x+1\,-2\,x^2-2\,x\right)$

$-2x+3$