There's really no "going rate." You'll find IA holders who will pencil whip your annual for three hundred dollars...every area has one. You'll find others who will be very thorough and your annual will come out at eight or nine thousand. You'll find others who will allow you to assist with the annual, and others who adamantly will not. Some will perform only the inspection and allow you to have the work done elsewhere, others will not.
Going rates, such as they are, range from flat-rate inspections of six hundred to twelve hundred, or fifty bucks an hour to one fifty an hour, depending on the nature of the inspection, or the work.
Bear in mind that especially where inspection is concerned, and this applies equally to an annual or to a special airworthiness permit or major repair or alteration (337, etc), generally more work rests in the research and paperwork than in the actual labor. Sometimes folks forget this when they see the bill...it's not just about attaching a few wires or riveting a patch as it is the qualification, the experience, the knowledge, and the behind-the-scenes effort, to say nothing of the liability.
A wide diversity exists in what you may expect to be charged, and your best bet is to approach the particular IA or repair station and inquire. You'll also find some who use flat-rate books for particular jobs, but you should also bear in mind that the nature of being an inspector means that one is constantly looking for defects, and when you go in to have a cylinder changed you may well end up needing an engine mount replaced...because more may be found than what you thought was wrong...and the cost may go up. Even with a flat-rate job, something as straight forward as a cylinder change, a failed stud or some unexpected finding may increase the amount of work, the complexity, and the cost. Additionally, by effectivity (part number and serial number), you may have a particular part which is subject to additional inspection requirements (eg, an AD) which also increase costs above what might normally be expected for that particular work or inspection item.