How do I submit a form in the correct osTicket REST API way?

It goes to a form that has date entries, a custom form made outside of osTicket, regular HTML form.

How do I submit it in the REST API form that osTicket accepts?

I am trying to get it into a format like:

/myplugin/mycontrolleraction/yyyy/dd/mm/yyyy/dd/mm

I then assemble those into a date for a given database.  But how do I submit it to osTicket in that way?  It's always going to have a regular querystring like ?year1=2016&month1=05day1=01&....