My trainer is always mixing things up. I'm not sure I've had an HIIT workout. My workouts are very much like Shriffron's at a much lower level. 2 workouts have 1 exercise where I lift heavy.
For example, After my warmup on Monday I did a circuit of 5 exercises-Bench Press @ 40lb (2-20 lb weights), 8 reps per side, DB reverse lunge swing pop w/8lb#, :30 ropes, 10 TRX Ice skater hops and 10 pull ups. I did 3 rounds that = 3 sets. I ended with the slideboard-8 sets of :20 slides with :40 rests. I was challenged to slide faster by counting the # of times I slid across the board.
Yesterday's workout was tiring. After warming up I did a circuit with 5 sets of 5 reps. I started with the RFESS-40# (2@20#), TRX Row, 10 Kettlebell swings, not sure of bell size, Landmine 1/2 Kneeling press, 35 #, and a sled push/pull @ 135 lbs. Then I tried a TRX 1 Arm 1 leg plank.
Tomorrow I after my warmup I will do 2 sets of 10 kettlebell swings then do an AMRAP (as many rounds as possible) workout. The workout consists of 8 reps of Cable Rotational Press, TRX Oblique Knee Tucks, Rope rotational slams and 4 TRX Resisted Torso Rotation, and rotational lunges. My goal for this workout is 6 rounds. I will end with the TRX plank series: Knee Tuck, Saw, Side Plank, 2 sets :20 ea.
My workouts vary and focus on what my upcoming activities are. In mid Sept I'm doing a 3 day 109 mile Mtn bike ride over 3 days. For example, I recently completed a bicycle tour in Wisconsin. I had 4 weeks of endurance work then 4 weeks of strength work before the tour. In the past I would have spent lots of time riding my bike. I doubt if I rode 50 miles before the tour. I rode 292 miles over an 8 day period. 2 of the days were 73 and 74 miles. Fortunately, they were not back to back. On the shorter days I thrived. On the 70 mile days I thrived until about 65 miles then survived the last 8 miles.
My gym is a small, private gym. The focus is functional fitness geared toward lifestyle needs. Squatting, lunging, push/pulls, etc. Very basic exercises. You work within your capabilities. I did not start at the level I'm working at now. I did mostly body weight exercises with bands and the TRX. I progressed when I was ready. My trainer will push me and challenge me but only when he thinks I can handle it. He's also a stickler on form.
There is no fancy equipment, kettlebells, weights, barbells, sled, slide board, ropes, TRX, cable machine, balls, sandbags, foam plyoboxes, bands, bosu, fit balls. They do offer spinning classes and 1 yoga class on Sunday. Even though they have the Bosu I've not used it, nor have I done any fancy balancing on the fitball. When I first started I used the fitball a lot but not so much now.
Unfortunately, functional fitness can mean many different things. I spent some time researching the various personal training certifications before I chose this gym. I read fitness gurus like Gray Cook, Dan John, Dr. Stewart McGill and others. I wanted to learn to use kettlebells but didn't have much success teaching myself. I also had an injury that I wasn't overcoming with PT so I had to be careful not to make the injury worse. The gym offered an introductory price that I took advantage of. I do semi-private training to reduce the cost but I often get 1-on-1 training.
My advice is to look at the trainers qualifications. The gyms focus, philosophy of training etc. If it's a big box gym or local rec center you may not find what you want. You may have to find a local, privately owned gym, expensive but well worth the investment.