Calculate Radial Fillamount

I want to “clamp” the filled amount of an image with 360° radial like this:

I have:

float max_amount = 500f;
float cur_amount = max_amount;
float minValue = 0.1f;
float maxValue = 0.35f;

cur_amount needs to be calculated to fit a radial circle segment fill from 0.1f(minValue) to 0.35f(maxValue).

How can i calculate the fillamount?
Normally i do this for the 360° complete circle.

float calc_amount = cur_amount/max_amount;

@OctoMan
your code was a great help thank you

//Otimized!!

Healthbar.fillAmount = (cur_amount/max_amount)*(maxValue - minValue)+minValue;

Hi, I am not sure whether my answer is what you want

using System.Collections;
using UnityEngine.UI;

public class test : MonoBehaviour {

    float min_amount = 0.1f;
    float max_amount = 0.35f;
    float calc_amount;
    Image image;
    public float input;


	// Update is called once per frame
	void Update () {


        if (input <= max_amount && input > min_amount)
            calc_amount = (input - min_amount) / (max_amount - min_amount);

        image = gameObject.GetComponent<Image>();
        image.fillAmount = calc_amount;

    }
}