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Compute the area under the graph of the "fractal" function
$$F(x)=\sum_{n=0}^{\infty} \dfrac{1}{2^{n}} \cos \left(3^{n} x\right)$$
over the interval $\left[-\dfrac{\pi}{4}, \dfrac{\pi}{4}\right]$. (It is known that this function is nowhere differentiable.)

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