So many Google features are deliberately accessible to external systems; you can do a Google search or generate a Google map or chart your data by passing a fully qualified parameter-inclusive URL (no clicking of buttons necessary).
How about Google Calendar? If your calendar-appointment data is in some other system, is there an URL-scheme such that when executed adds an event on a specified date to a specified person’s calendar, so that you can loop through your other system and populate Google Calendar with the data that’s in your other system?