A car rental company has established a rental fee policy, which includes a base fee of $$30$ plus an additional $$5$ for each day a rental vehicle is returned past the due date. Additionally, there is a penalty of $$50$ for any rental returned more than a week $(7$ days$)$ late. Write a function named calculate$\_$late$\_$fee that takes a non$-$negative integer $($num$\_$late$\_$days$)$ indicating the number of late dates as input, and outputs an integer indicating the total rental fee using the given policy.