That's a Circle, right?

Geometry Level 5

Above is the graph of the equation x2+y22x+8+2y=16x^2+y^2-|2x+8|+2y=16 If the area of the figure is denoted AA, then find 1000{A}\lfloor1000\{A\}\rfloor


Details and Assumptions
{N}\{N\} denotes the fractional part of NN.
In other words, {N}=y\{N\}=y where N=x+yN=x+y, xx is an integer and 0y<10\le y < 1.

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