I've edited your original post to remove the swearing.  Please refrain from swearing, we're here to help, but there's no need for strong language.

First of all - there is an example on that page of creating a web services function

Each project has its own requirements for what an API needs to do, so there isn't so much of an existing web services API, it is a framework that allows you to easily build your own, which is explained in the document.

Secondly:

Examples of source code for mobile apps

We are not mobile developers and this isn't a mobile platform.  The web services acts as an endpoint.  How you interact with it depends on the programming language being used.  If you need support for coding a mobile app you should seek support in a forum for mobile developers.