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CODE:
Int(Int(sqrt(1+piecewise(x^2+y^2 < 400, -(1/9)*x, -85 <= x and x <= 85 and -85 <= y and y <= 85 and 400 <= x^2+y^2, -(10240000/9)*x/(x^2+y^2+2800)^2-2000*x/(x^2+(170-y)^2+2800)^2-(1000*(-340+2*x))/((170-x)^2+y^2+2800)^2-(1000*(-340+2*x))/((170-x)^2+(170-y)^2+2800)^2-2000*x/(x^2+(170+y)^2+2800)^2-(1000*(340+2*x))/((170+x)^2+y^2+2800)^2-(1000*(340+2*x))/((170+x)^2+(170+y)^2+2800)^2-(1000*(-340+2*x))/((170-x)^2+(170+y)^2+2800)^2-(1000*(340+2*x))/((170+x)^2+(170-y)^2+2800)^2)^2+piecewise(x^2+y^2 < 400, -(1/9)*y, -85 <= x and x <= 85 and -85 <= y and y <= 85 and 400 <= x^2+y^2, -(10240000/9)*y/(x^2+y^2+2800)^2-(1000*(-340+2*y))/(x^2+(170-y)^2+2800)^2-2000*y/((170-x)^2+y^2+2800)^2-(1000*(-340+2*y))/((170-x)^2+(170-y)^2+2800)^2-(1000*(340+2*y))/(x^2+(170+y)^2+2800)^2-2000*y/((170+x)^2+y^2+2800)^2-(1000*(340+2*y))/((170+x)^2+(170+y)^2+2800)^2-(1000*(340+2*y))/((170-x)^2+(170+y)^2+2800)^2-(1000*(-340+2*y))/((170+x)^2+(170-y)^2+2800)^2)^2), x = -85 .. 85), y = -85 .. 85)

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