A car rounds a flat curve and experiences a centripetal force directed toward the center of the curve and perpendicular to the direction of its motion. If the driver of the car doesn't hit the brake OR the gas, how will the curve affect the motion of the car?

If a car is rounding a flat curve, it experiences a centripetal force that pulls it towards the center of the circle it is rotating in.

Now,

The centripetal force can be balanced by the centrifugal force caused due to the acceleration of the body at the high speed which counters the centripetal force and in turn prevents the car from slipping down the curve.

So,

If the car doesn't hit the gas then the car will fall down from the curve as the Centripetal force will exceed the Centrifugal force of the car.

However, if the car doesn't hit the brake then the car will maintain it's position on the flat curve track as the centrifugal force will counter the effect of centripetal force directed towards the center.