Your example seems to prove just the opposite, i.e. only in trivial applications such as web search client API is the API design trivial compared to the implementation. In complex systems, such as programming languages, IDEs, operating systems and scalable search engines, good API design is paramount to managing complexity.

Some good discussion on API design: http://lambda-the-ultimate.org/node/3720 http://www.infoq.com/articles/API-Design-Joshua-Bloch