The term 'with great intensity' can be described using the crossword solutions 'rabidly', 'DEEPLY', 'KEENLY', and 'likemad'. Rabidly means to do something with extreme enthusiasm or passion, DEEPLY implies a strong and profound feeling, KEENLY suggests an intense focus and concentration, and likemad is an informal phrase that means to do something with great energy and enthusiasm. All of these words describe the same concept of doing something with great intensity.