Using the definition of the operation $\S$, we have $7\,\S\,2 = 3(7) + 5(2) = 21 + 10 = \boxed{31}$.
The answer is: 31
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Define the operation $\S$ as follows: $a\,\S\, b=3a+5b$. What is the value of $7\,\S\,2$?

### Answer:
