The mathematical expression in the image is quite complex. Let's break it down into its different parts and analyze it:

$\sum_{i=0}^{10} \frac{i}{\cos\left(\frac{1}{10}\right)} \cdot \frac{11}{100} - \int_{-2\pi}^{2\pi} \frac{37}{10} \, dx$

This is subtracted from:

$\frac{1}{\sqrt{\ln\left(100 \coth\left(\frac{\pi}{5}\right)\right)} - \left(\sin^2(z) + \cos^3(z)\right)}$

Step-by-step breakdown:

1. Summation: $\sum_{i=0}^{10} \frac{i}{\cos\left(\frac{1}{10}\right)} \cdot \frac{11}{100}$

   • This is a summation where $i$ goes from 0 to 10. Each term is multiplied by $\frac{11}{100}$ and divided by $\cos\left(\frac{1}{10}\right)$.

2. Integral: $\int_{-2\pi}^{2\pi} \frac{37}{10} \, dx$

   • This is an integral of a constant value $\frac{37}{10}$ over the interval $[-2\pi, 2\pi]$.

3. Complex Denominator: $\sqrt{\ln\left(100 \coth\left(\frac{\pi}{5}\right)\right)} - \left(\sin^2(z) + \cos^3(z)\right)$

   • The denominator involves a logarithmic term combined with a hyperbolic cotangent function ($\coth$) and the trigonometric expressions $\sin^2(z)$ and $\cos^3(z)$.

Next Steps:

• I'll proceed to evaluate each component of this expression to obtain a final simplified form. Shall I go ahead with that?

If you'd like details on a particular part of the expression, feel free to let me know.

Questions:

1. Would you like to see the expanded form of the summation term?
2. Should I evaluate the integral step-by-step?
3. Would you like an explanation of the hyperbolic cotangent ($\coth$) function?
4. Should I provide a graph or visualization of the trigonometric functions involved?
5. Do you want further clarification on logarithmic expressions in the denominator?

Tip:

In complex expressions, breaking down each section and solving in parts is crucial to avoid mistakes and better understand each term's contribution.