Subscription billing with proration and tiered usage

Build a small billing engine that produces each user's charge for one 30-day cycle. Amounts are in cents, and the final charge per user is rounded down only once, at the end.

1. Every user has one or more fixed-price subscriptions. Return each user's monthly total.
2. Users change plans part-way through the cycle. Prorate: charge the old price for the days before the change and the new price for the rest.
3. Add usage-based billing. Some metered items have a flat price per unit; others are tiered, where each block of units has its own price. A user may have usage without any subscription.

Each part builds on the one before, so structure the code to be extended.