Can you find a general rule for this? - Part (2)

Calculus Level 4

If \(x,z\) are real numbers with \(z > 0\), there exist unique integer \(m\) and real number \(r\) with \(0 \le r < z\) so that \(x = mz + r\). Define the remainder \(\{x \text{ mod } z\}\) as the value of \(r\) for the corresponding \(x,z\).

Compute \[6 \int_0^2 \{x^2 \text{ mod } x\}\,dx\]

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