Let $f$ be a twice differentiable function on $R$. If $f^{\prime}(0)=4$ and $f(x)+\int_0^x(x-t) \quad f(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x$, then $(2 a+1)^b a^2$ is equal to $\_\_\_\_$ .
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