Evaluate the defined function. Express your answer as an integer or simplified fraction. If the function is undefined at x=6, select Undefined.

The given piecewise function is:

$$f(x) = \begin{cases} -2x - 2 & \text{if } x \le -5 \\ 2x^2 + 2x & \text{if } -5 < x \le 5 \\ \frac{3}{4}x - 1 & \text{if } x > 5 \end{cases}$$

For $x=6$, we check which condition it satisfies:

• $6 \le -5$ is false.
• $-5 < 6 \le 5$ is false.
• $6 > 5$ is true. So, we use the third expression: $f(x) = \frac{3}{4}x - 1$.

$$f(6) = \frac{18}{4} - 1 \\ f(6) = \frac{9}{2} - 1 \\ f(6) = \frac{9}{2} - \frac{2}{2} \\ f(6) = \frac{7}{2}$$

The value of the function at $x=6$ is $\boxed{\frac{7}{2}}$.