It's called "short-rate" cancellation.
In Alberta, all auto policies automatically renew (I think the insurance companies are legally obligated to do this) whether or not you have paid them. So technically if you cancelled the policy three days in, you will be subject to the short-rate tables. At three days I think the total charge is something like five or six percent (I can look it up on Monday if you want) but $350 would mean your annual premium is crazy high.
Did you get coverage somewhere else ON YOUR RENEWAL date? If so you may be able to get your broker to re-process your cancellation effective of your renewal and avoid the penalty.
"Masked Bandit is a gateway drug for frugal spending." - Unknown303