Is the United States an indirect democracy or a republic?
The answer to this question is going to depend almost completely on how your book defines a republic. As the link below tells us,
there is no consensus among scholars ... as to exactly what a republic is.
Given this fact, it is very hard to say if the United States is a republic or an indirect democracy.
In many ways, the United States is an indirect democracy. The people of the United States do not tend to vote directly on proposed laws. Instead, they elect representatives who do vote directly on the proposals. This is how an indirect democracy works.
However, by some definitions, the US is a republic and not an indirect democracy. By those definitions, a democracy is one in which the people have absolute control. By comparison, a republic is a form of government in which there is a constitution or some other sort of basic law that limits what the people can do. By this definition, the US is clearly a republic and not a democracy because there are limits on what sorts of laws the people can make.
It is very difficult, then, to answer this question without knowing exactly what definition of "republic" we are using. In layman's terms, the US is both a republic and an indirect democracy. However, depending on the exact definition used, one can arrive at different answers to this question.