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But since the line \(y = x + 2\) cuts the circle from top-right to bottom-left, the region enclosed is actually the smaller segment. Hence, the area is:
oxed{ rac{16\pi}{3} - 6\sqrt{3}}
Question: Find the remainder when \(x^4 + 3x^3 - 2x^2 + x + 5\) is divided by \(x^2 - x + 1\).

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