Pass custom variables to a case

Is there anyway you can pass custom variables to a case via the Web API? I am not seeing anyway to do it in the documentation.

I am trying to start a case and pass data to it that is needed for the workflow behind it. Please help.

I am using Bonita 6.3 Web API

In the official documentation you can find an example about creating a new case and, in the same API call, settings process data values: http://documentation.bonitasoft.com/web-rest-api-examples#start_case_with_variables

Or you can do the same in two API calls:

If documentation is not enough feel free to ask for more details.