Slightly inflated square

Geometry Level 4

The figure above consists of 4 identical intersecting quadrants inside a square of side 4. The area of the shaded region can be expressed as abπ+cde\frac{a}{b}\pi+c-d\sqrt{e} for positive integers a,b,c,da,b,c,d with ee with aa and bb are relatively coprime, and ee is square free.

Evaluate the value of a+b+c+d+ea+b+c+d+e.

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