I want to develop one simple api using php.
My functionality is that if some one enter some required values then they will get calculation result from the algorithm
It sounds like you want to create a web-service that other people can connect to, send answers and retrieve a result.
If that's the case, you've got three options, SOAP, XML-RPC and REST. If it's a simple API, SOAP (and probably XML-RPC) will be overkill - you don't want to have to create a WSDL file, install a SOAP server library (although, Zend_Soap is decent enough). REST on the other hand will allow anyone to easily consume your API.
Let's look at an example, say you want to provide a simple "sum" service (i.e., add a few numbers), you could have a URI scheme like this:
http://example.com/sum
to sum the numbers 5, 8 and 9 your web service users would simpy execute an HTTP GET to
http://example.com/sum/5/8/9
let's pretend for a moment that summing is actually a very computationally expensive task, by using REST and a GET you can take advantage of HTTP caching so that your server isn't constantly hit when someone sends the same parameters for calculation.
If your web service has a resource that isn't side-effect free (i.e. it changes something in a database) you should use PUT, POST or DELETE (PUT for updates, POST for creating and DELETE for delete) as the HTTP specs state the GETs shouldn't have side-effects. Similarly, PUT and DELETE should be safe to repeat if you get an error back or the network connection times out.
There's a good talk (video and slides) on REST here: http://www.parleys.com/display/PARLEYS/Home#talk=31817742