Mac OS X 10.9 - setting permanent environment variables

Drop the $(...) bit, which would attempt to execute the command within the brackets and set $MULE_HOME to whatever it produces. In your case /opt/mule-standalone-3.4.0 is not an executable, hence the error you are getting.

export MULE_HOME=/opt/mule-standalone-3.4.0

and use ~/.bashrc not ~/.bash_profile.

EDIT: It seems opinion is that you should set environment variables in your ~/.bash_profile script, and not ~/.bashrc script.

Just did this really easy and quick. First create a ~/.bash_profile from terminal:

touch ~/.bash_profile

then

open -a TextEdit.app ~/.bash_profile

add

export TOMCAT_HOME=/Library/Tomcat/Home

Save document in TextEdit and you are done.