Although your trainer may claim to have invented certain exercises, chances are if his name is not "Arnold" or Georg Hackenschmidt, he didn't invent it. Many of us modify exercises, but few create them. The "Hack Squat" created by Hackenschmidt is one of a multitude of squats that you can use to diversify your lower-body training. It primarily targets your quadriceps but employs the glutes as synergists and the hamstrings as dynamic stabilizers. You can perform this exercise on a machine or with a barbell.
To try the barbell version, place a barbell on the floor just behind your legs. With your feet flat on the floor and shoulder-width apart, squat down hinging at your hips and grab the barbell with an overhand grip.
With your weight in your heels, raise up just prior to full extension and then descend again until your thighs are parallel to the floor. Keep your arms and back straight and your shoulders lifted throughout the exercise. Repeat for 12 to 16 repetitions.