### Instruction: Define $a * b$ as $2a - b^2$. If $a * 5 = 9$, what is the value of $a$?### Response: This problem involves a non-standard operation, so I need to follow the definition carefully.
I know that $a * 5 = 9$, so I can plug in $5$ for $b$ in the definition and get $2a - 5^2 = 9$.
Simplifying, I get $2a - 25 = 9$.
Adding $25$ to both sides, I get $2a = 34$.
Dividing both sides by $2$, I get $a = 17$.