# Plot above desired region

I would like to plot a real-valued function $f$ of two real variables $x,y$ but only over the region of the $x$-$y$ plane satisfying \begin{align} x>0, \qquad -x^{3/2} < y < x^{3/2}. \end{align} Is there a straightforward way to do this using Plot3D?

-

RegionFunction option is what you're looking for:
Plot3D[Cos[x] + Sin[y], {x, -1, 5}, {y, -5, 5},