Final answer:
The capital of Idaho is Boise, which is also the most populous city in the state and serves as its cultural, economic, and political center.
Step-by-step explanation:
The capital of the state of Idaho is Boise. Boise is not only the capital but also the most populous city in Idaho. The other cities listed, such as Idaho Falls, Pocatello, and Coeur d'Alene, while being significant cities within the state, do not hold the status of the state capital. Boise serves as an important cultural, economic, and political center in Idaho.