Write a shell script (bash) called birthday. It will accept a date in the format of 'mm/dd/yyyy'; however, this input format should not require any validation. Nevertheless, you are required to check whether the first parameter is provided; if not, display the usage of birthday script. Your script must be able to do the following:
1. If it is a leap year display "YYYY is a leap year", else display "YYYY is not a leap year" where YYYY is the input year.
2. Display the day of week (Monday, Tuesday,..,Sunday).
3. Display the number of days before or after your birthday this year.
4. Display your age.
5. Display a calendar on input date.