“How can I help you, officer?” sounds pretty dang civil to me.

It's trolling. You know he's only going to repeat his own question.

I see it as a polite way to redirect the conversation. I usually respond similarly -- although not that exact wording. From what I can tell it's never agitated the cop, and they've never insisted that I answer their question. They just move on with the traffic stop. Sometimes I get a ticket, sometimes I don't.

So how do you answer the cop's question(s) politely such they even let you go?

You don't. If they want to give you a ticket, you're getting a ticket. If they want to let you off, they'll let you off. If they want to drag you out of your car and beat you half to death, you're getting beaten half to death. The only thing you can possibly do is make the situation worse. Police are the violence arm of the state. You're not in control, and your rights, along with your life, depend on their whim.

> Police are the violence arm of the state.

It should be stressed that it's not so in every country

"by opening your trunk. Thanks for offering"

Sounds all good and fine until you meet someone on a power trip on a bad day and fit in a bucket they don't like. But in those situations at least what you describe can act as damage control.

The number one rule of talking to cops is don't talk to cops. Don't be an ass but don't say more than you absolutely have to. It may just be a job for them but that doesn't mean their job can't involve ruining your day if they think they can use you to meet their quota - your interests literally don't align.

I barely trust police officers in my own country and those actually need to go through multiple years of formal training before being let loose on society and end up in a world of bureaucratic hurt if they as much as think about pulling out their gun. Incidentally they also don't have to chase after random people for speeding because we have radar cameras for that.