heart rate jumps during exercise

I have exercised my whole life. I used to run 7 miles 3 days a week. Until I hurt my foot. I quit smoking 10 years ago. I am 41 years old.Is it normal for my heart rate to jump up to 175 during exercise? I am not sure if the machines at the gym are really telling me my true heart rate. I also notice that when I do my cardio and  my weight training class I feel like my heart is beating out of my chest. But as soon as we stop the jumping jacks and slow down my heart will go back down. Is this normal? I also noticed before when I was walking in the mall and decided to use the steps after climbing up them I could feel my heart rate jump up. I am not overweight, and have a good low blood pressure. I asked my doctor but he did not seem to concerned because I am only 41. I am getting worried. Any help would be great!

[Jokerthered]

Yeah I have a pretty good idea what might be.  Get a quality personal heart rate monitor.  If the machines are right you need to get a referral to a specialist because only after an official diagnosis on your medical records is it going to be treated.  Although in your highly fit case, right now treatment options might not be to your liking but those are conversations netween you and the specialist.  

[Dr Arora]

Hi, according to your age a heart rate of 140 to 150 you the target heart rate during exercise and you are achieving that target during most of the exercises. If you are sure about the machines in the gym reading a heart rate of 170, there is nothing to worry as your maximum heart rate can be around 180 during exercise. Sometimes the exercise machines are not much reliable in detecting the heartrate. You may note your heart rate by counting the pulse for one minute immediately after doing exercise. I hope this helps