I break into houses for a living, so yeah, I get the cops called on me from time to time. (I manage, service, and sell real estate, mostly foreclosed properties) I usually call the police beforehand if I have to get too creative in gaining access to one of my properties, or if I'm working after dark.
My assumption in any police interaction is that I will be facing a judge on some sort of charge; that I will have to explain my actions in a court of law. Many of the properties I service have signs of illicit drug use or manufacture. The previous occupant might have left weapons used in a crime. Diabetics leave 1cc syringes all over the damn place. I carry equipment that I use to break into houses. If a cop gets it into his head that he wants to arrest me, he can point to all kinds of things for probable cause to justify himself, so my objective is not to stop him, but to ruin any ability for him to prosecute me, and in doing so, hopefully compel him not to waste my time.
Getting riled up or upset with the cop doesn't help me win that court case, it just tells the judge that I was antagonistic. Direct confrontation leads to handcuffs and expensive fines. Giving up all my rights and giving the cop anything he wants doesn't help my court case either. The best way to deal with overtly aggressive people - and a cop who suspects you're a criminal is usually fairly aggressive - seems to be passive aggression. You paint the picture of someone who is completely cooperative, while building your case quietly, subtly, and let the cop come to believe he's in the wrong before he thinks you realize he's in the wrong.
But in the several cases I've had chance encounters with police, the only problem I had was with a retired trooper who wasn't aware that Ohio was an Open Carry state. He thought that a "concealed handgun license" meant that the bearer was required to carry concealed, rather than allowed to carry concealed. I think it's a heck of a lot easier interacting with law enforcement while carrying than without, provided you follow the rules. Cops seem less in-your-face aggressive now than they did before I went about armed.