UPD:
After talking over phone with the main garage (luckily they are located in my city) today i took the car there, and they replaced the battery without any problem, a think it's too soon to talk about changes - drove the car from garage to home it;s like 4-5 miles , all the way is inside city. I'll see next couple days how it's going and update you.
Thanks you all for your advices, especially Smurf .

 

How much does a battery cost?

 

I don't know what it costs Honda, but if we had to buy it the cost is about $2500....

 

I had my battery on my 06 replaced at around 60K miles last year...the IMA charge indicator was all over the map and would run down to below 2 bars frequently providing no assist in warmer weather and with the AC on. Mileage as well began to decrease noticeably (20%) though i couldnt tell if the new Michelin X low rolling resistance tires which were replaced at that time was contributing to the problem. After the battery was replaced and the software updated these issues still exist and drivability is worse as i understand the software has been changed so that the battery is less 'stressed' so i get almost no assist on uphills or even slight grades..engine races (4k and above). IMA indicator is still all over the map...starts out full charge..go a few miles..down to 2 bars...back to 6..etc and mileage is subpar...around 28 city and 34-36 highway...previously earlier in the life of the car i averaged 45+ combined. I havent pursued Honda since the battery was changed as i just gave up but I'm curious to see if there are any fixes which at least in my experience seems to be due more to the software than the battery going bad.