Sound mysterious, I am using both using numpy and matlotlib quite regularly. The only things I can say are:
* The polar plot example runs fine for me in both Python enviroments.
* ~~What you told us about the exception is a bit confusing since neither numpy nor matplotlib have an init.py file afaik (they have both multiple __init__.py files though)~~ edit: I just realized that you were probably only struggling with the forums markdown interface since your init.py is printed bold (you have to escape the first two underscores: \_\_init__.py).
* The polar plot example does not import anything from numpy.random and neither does matplotlib.pyplot.
I cannot think of anything obvious, I think you will have to describe more precisely (actually copy and paste the full trace of the exception) what you are doing and what is going wrong.