Calculate Dasher Pay from Delivered Orders

Problem: Calculate Dasher Pay from Order Time Ranges (with Mock Service Call) You are given an external service that, for a given dasher_id, returns a list of delivered orders with their delivery time ranges: start_time: when the delivery work for an order started end_time: when it ended You are also given a per-minute pay rate rate_per_minute. Compute the total pay for the dasher. Requirements Implement a function/module that retrieves the order ranges via a mock API/service call (no real networking needed; just simulate the service response in code). Compute and return the total pay based on the returned time ranges. Base Pay Rule Duration of an order is end_time - start_time (in minutes). Total pay = (sum of all order durations) × rate_per_minute. Follow-up (Overlapping Ranges) If a dasher can accept multiple orders concurrently and the time ranges overlap, implement a version that computes pay based on the actual working time by taking the union of all time ranges (i.e., do not double-count overlapping minutes). I/O Contract (suggested) Input: dasher_id (string/int), rate_per_minute (int/float) Service output: list of ranges [(start, end), ...] where times are comparable (e.g., integer minutes from 0 or timestamps) Output: total pay (numeric) Constraints Number of orders n: 1 ≤ n ≤ 2e5 Times are integer minutes (assume basic validation by the service) Example Test Cases (minute indices) Non-overlapping: [(0,10),(20,30)], rate=2 → pay=40 Overlapping (union): [(0,10),(5,12)], rate=3 → union=12 mins → pay=36 Containment: [(0,10),(2,5)], rate=1 → union=10 → pay=10 Touching: [(0,10),(10,15)], rate=2 → union=15 → pay=30 Mixed: [(1,4),(2,6),(8,10),(9,12)], rate=5 → union=9 → pay=45 Example Input d2 2 Output 40