I am mostly playing around with creating command line c++ applications, using the console for input and output display.
I wonder if there is any "simple" way to create a web client interface on top of a simple c++ program, requesting data input and to display results on a web page (perhaps similar to java).

For example, if I wrote a simple calculation program and would like to display it on a web page. I gather I would need to place the c++ program in a web server directory and revoke/call it from a html page (client). I am not sure if any of the available free IDE's that support this type of setup/functionality?
Would this be possible (assuming a beginner/intermediate level)?

An IDE (Integrated Development Environment ~= text editor+compiler+code browser+linker+debugger etc bears no relation to the desired functionality.

There are lots of methods to do that (besides OS-specific connections of program console i/o to the remote terminal client). For example, you may write your program as CGI (or better FastCGI) requests handler. Probably, the most expressive way to go: make your program as http server. Have a look at dlib library:
See http server example: http://dclib.sourceforge.net/server_http_ex.cpp.html
Some tens of lines - and your C++ console program turns into the real web-server ;)

commented: great links to have fun with for a beginner :-P thanks! +2