Using plugin_dir_path() with WordPress on MAMP

I’m not sure why this isn’t working for you.

I usually set the plugin path constant using dirname(FILE)

You could try:

define('MR_PLUGIN_PATH', dirname(__FILE__));    

//echo MR_PLUGIN_PATH;
include_once(MR_PLUGIN_PATH.'/phprets.php'); 

Also:

Are you sure phprets.php exists. You say you have phrets.php (missing the p)