How to realize the function $\bar f(x)=\frac{1}{2\pi}\int_0^{2\pi} f(x,\theta)\;d\theta$?

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Maybe this sounds quite silly and maybe I should take a break from math during Christmas and I apologize in advance, but how should I realize this function:

$$\bar f(x)=\frac{1}{2\pi}\int_0^{2\pi} f(x,\theta)\;d\theta$$

In principle, this seems as an average value to me but average value over an angular interval (if such a term exists)? What is the role of $x$? Is this function somehow independent of radius?

Any help will be much appreciated! Many thanks and happy holidays!