Tracking P.T Sessions

I would log it as "circuit training".

I do the quick track by just adding training and the amount of time. My trainers kick my butt too twice a week and I am easily huffing and puffing by the end of the workout. I don't count calories.

I am unsure how to track my personal training sessions with my trainer. She tries to keep my heart rate up for the whole hour, sprinting around the block, running stairs, jumping jacks, no resting between moves etc.
I work up a pretty good sweat, but we mostly focus on lifting weights and building muscle mass. Should I try and count this into my daily cardio/workout tracker? What should I track it as?
I feel as though I should track it as calories burned since I usually work up a pretty good sweat and I'm exhausted by the end of the hour, therefore I am obviously expending some calories.