How plot $f(x,y) = \frac{x}{1-y}$ with $x^2+y^2<1$?

Question

How do you plot $$f(x,y) = \frac{x}{1-y} \text{with}~ x^2+y^2<1$$ in Mathematica or Maple?

Answer 1

In Mathematica (version 6 or newer)

Plot3D[x/(1 - y), {x, -1, 1}, {y, -1, 1},
       RegionFunction -> Function[{x, y}, x^2 + y^2 < 1]]

Answer 2

In Maple, you can use the following codes:

[> with(plots):
  plot3d(x/(1-y), x = -1 .. 1, y = -sqrt(1-x^2) .. sqrt(1-x^2), axes = boxed, filled = true,numpoints = 1000,color=green);