Folks here is basic software engineering principals at work. Yes, you could do this work in F5 LTM but why would you want to? The server is setup to do this type of mapping which is static insteading of adding complexity to iRules.
Here is how do you it with IIS server....
http://www.zorched.net/2006/01/20/aspnet-web-application-without-aspx-extension/
(This is older code).
We can change the extension of any .NET file.
To change the extension of .aspx file
Open IIS->Default Website -> Properties
Select HomeDirectory tab
Click on configuration button
Click on Add
Browse the aspnet_isapi details in to the Executable textbox
The file may be in
(C:\WINDOWS\Microsoft.NET\Framework\v1.0.3705\aspnet_isapi.dll)
OR
(C:\WINDOWS\Microsoft.NET\Framework\v1.1.4322\aspnet_isapi.dll)
Now add he new extension into Extension textbox
eg:- .chaos
Now change Verbs to Limit to and add
GET,HEAD,POST,DEBUG into Limit to text box
Open machine.config file add the new extension under tag
Now you can create pages with .chaos extension.