When does the auto_arima model uses max_d and max_D in pmdarima Python?

Question

I use auto_arima to find the best values for p, d, q, P, D, and Q. After trying many times, I notice something strange (At least for me, because I'm new to Forecasting. ) regardless of the data and other parameters, auto_arima only uses the value of d, D it seems the value of max_d and max_D is useless. My questions are:

1. When max_d and max_D will be used? (try values between d or max_d)
2. Why do p and q starts with start_ but d does not?

Below is my code sample and the output:

BEST_MODEL=auto_arima(

    df,
    
    d=0,max_d=2,
    start_p=0,max_p=5,
    start_q=0,max_q=5, 
    
    D=0,max_D=2,
    start_P=0,max_P=5,
    start_Q=0,max_Q=5, 
    
    m=7, 
    seasonal=True,
    error_action='warn',
    trace=True,
    supress_warnings=False,
    stepwise=False,
)