To solve this optimization problem, we need to define variables and constraints based on the given conditions. Let's denote:

- $A$ as the number of algebra questions answered,
- $C$ as the number of calculus questions answered.

The objective is to maximize the total score, which can be calculated as $A + 3C$, since each algebra question is worth 1 point and each calculus question is worth 3 points.

Given constraints are:
1. $A + C \leq 25$ (at most 25 questions can be answered),
2. $A \geq 10$ (at least 10 algebra questions must be answered),
3. $C \geq 6$ (at least 6 calculus questions must be answered),
4. $A \leq 15$ (no more than 15 algebra questions can be answered),
5. $C \leq 15$ (no more than 15 calculus questions can be answered).

Since all answers are assumed to be correct, we aim to find the values of $A$ and $C$ that maximize the score under these constraints.

The reasoning behind solving this problem involves recognizing it as a linear programming problem. The Gurobi Python interface will be used to model and solve this optimization problem.

```python
from gurobipy import *

# Create a new model
m = Model("Math_Contest")

# Define variables
A = m.addVar(lb=10, ub=15, vtype=GRB.INTEGER, name="Algebra_Questions")
C = m.addVar(lb=6, ub=15, vtype=GRB.INTEGER, name="Calculus_Questions")

# Objective function: Maximize the total score
m.setObjective(A + 3*C, GRB.MAXIMIZE)

# Constraints
m.addConstr(A + C <= 25, name="Total_Questions")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Maximum Score: {m.objVal}")
    print(f"Algebra Questions: {A.x}")
    print(f"Calculus Questions: {C.x}")
else:
    print("Model is infeasible")
```