In the function \( f(x) = 10x + 15 \), \( f(x) \) represents the total cost of renting the bicycle, \( x \) represents the number of hours the bicycle is rented, and the term \( 10x \) represents the hourly fee of $10 per hour.
The constant term in the function, which is \( 15 \), represents the flat rate fee that Cesar pays regardless of how many hours he rents the bicycle.
Therefore, the flat rate for the bicycle rental is $15.