I have a 2D mapping of some field that is parametrized by $x$ & $y$, $F(x,y)$. I want to integrate the values of the field that lie within a circle of radius $r$ and centered at $(x,y)$. How shall I formulate? I am interested in formulating the problem only. The following figure provides illustration.
Note: The field is a blackbox function so we cant evaluate integral directly.