That's not really how airline faring works. If you doing one-way or roundtrip searches, there will generally only be one fare component in each direction as pricing is based on origin and destination (they do not charge per segment ). If you book something like DTW-LAX, there are a set of AA DTW-LAX fare filings that apply to that route even though AA has no non-stop DTW-LAX flights (example shown below). On domestic fares when performing multi-city searches, generally anytime you choose a layover greater than 4 hours at an airport, you will create a "stopover" and a fare break adding an additional fare component. For most international fares (except Canada), a fare break and stopover occurs when you have a layover greater than 24 hours (although international fares can have a stopover allowance, with a fee on cheaper fares, while domestic fares almost never do -- except for Hawaii fares).

AA site will list out fare basis codes involved with fare components at booking at fare rules link, but not the pricing of each fare component. If you price out on ITA Matrix, it will list both fare basis codes and pricing (before various taxes and fees) of each fare component. There is a 7.5% US Excise tax on domestic fares. There is also a TSA tax (currently $5.60 each way), a US segment tax on domestic fares (currently $4.80 per segment increasing by .10 per year), and passenger facility charge (mostly $4.50 max allowed by law per airport, but some airports charge less than max -- CLT PFC is $3.00).

Note that going from a non-stop to connecting itin adds $4.80 segment tax and $4.50 (mostly) PFC to itin even if base fare is exactly the same.