The Shortcode Callback plugin allows you to use a [callback] shortcode to execute arbitrary PHP code wherever the shortcode is used.
Usage
Execute someFunction() and insert whatever it returns with the following shortcode: [callback function="someFunction"]
Example shortcode to include a PHP file (the path is relative to WordPress' ABSPATH), then insert the results of someFunction() where you used the shortcode: [callback include="custom/filetoinclude.php" function="someFunction"]
Shortcode example that includes a PHP file (the path is relative to WordPress' ABSPATH), then passes a paramter to someFunction() and returns the results where you used the shortcode: [callback function="someFunction" include="custom/filetoinclude.php" param="something"]
The format to call a class/method with the shortcode is exactly the same as above, except you specify the class::method in the "function" attribute of the shortcode. [callback function="someClass::someFunction" include="custom/filetoinclude.php" param="something"]
There is an example (with PHP code) over here.