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Polar Derivatives

The last Problem of the Week for 2011 is now posted, and it's feeling all festive. Take a journey deep into the cold, barren wastelands of the Northern ice cap and search among the iceburgs to find a certain toymaker's workshop. (In case you need help calculating the derivative of a polar equation.) 

With a nod of his head and a wink of his eye, he will promptly ask you to stop trespassing, and for Christmas this year? A restraining order from Santa. 

No, this is not how you planned things at all...