Suppose we have a restricted version of Python where function names must satisfy certain conditions:

A function name can only use lowercase letters $($a$-$z$)$ and underscores $(\_).$

A function name must start with a lowercase letter.

The length of a function name must be at least $3$ characters and no greater than $10$ characters.

Let $F$ be the set of all valid function names in this restricted version of Python.

$($a$)$ Let F$0$ be the set of strings satisfying the first $3$ conditions above;.

Provide a regular expression for F$0.$