Since the gym is probably open on the weekends, 10 days likely means 10 calendar days (to include weekends). If you want to continue working out there or try a new trainer, you might try to address your concerns with management and try to work something out. As far as cancellation without penalty goes, you certainly can ask if they will cancel based upon the unkept promises but I think you may have some push back because you had at least several full days with the unkept promise and the gym had no notice of your complaint until now.
The best place to start is by reading the contract itself. Very often contracts will contain terms that are more restrictive than would normally be the case if the contract were silent. The best course of action is to let the management of the club know of your concerns immediately. Very often a business will make exceptions to their policies in order to keep your good will.
Any legal issue can be complex and the answer can vary by jurisdiction. Before taking any action, you should consult an attorney who is licensed to practice in your area. The answer above is not meant to be legal advice but should serve as starting point for you to contact any attorney to review all of the facts and give you a legal advice based having the complete picture.