identify the "captain of industry" who led American business in the late 1800s and describe how they increased their wealth and power

Well there are several and whether you argue they are robber barons or captains of industry is up to you. One that comes to mind is andrew carnegie who owned a large portion of the steel industry, or rockefeller who owned most of the oil industry, or Vanderbilt who owned railroads. They each bought their competitors until they slowly owned more and more of the market to increase their wealth, and bribed many officials and practically held power over the government

It might be the second one