Evaluate the following integral.
\[
\int_{\ln (3 \pi / 2)}^{\ln (11 \pi / 6)} 10 e^{v} \cos e^{v} d v
\]

Step 1 ：Given the integral \(\int_{\ln (3 \pi / 2)}^{\ln (11 \pi / 6)} 10 e^{v} \cos e^{v} d v\)

Step 2 ：We can use the method of substitution. Let \(u = e^v\), then \(du = e^v dv = u dv\). So the integral becomes \(\int 10u \cos(u) du\) from \(u = 3\pi/2\) to \(11\pi/6\)

Step 3 ：We can solve this integral by using the method of integration by parts, where we let \(u = u\) and \(dv = 10 \cos(u) du\). Then \(du = du\) and \(v = 10 \sin(u)\)

Step 4 ：The formula for integration by parts is \(\int udv = uv - \int vdu\)

Step 5 ：After calculating the integral, we substitute the limits of integration back in to get the final answer

Step 6 ：The final answer is \(\boxed{5\sqrt{3} + \frac{35\pi}{6}}\)