What action is vital after completing APU maintenance?

Testing the APU under load after completing maintenance is essential because it verifies that the Auxiliary Power Unit is functioning correctly and efficiently under conditions it will face during actual operation. This step ensures that all repairs or adjustments made during maintenance have been effective and that the APU can provide the necessary power without any issues when required. This testing process can identify any potential operational problems that may not be apparent when the APU is run without load, thus ensuring safety and reliability for future operations.