ID: 778
Given a set of complex equations, extract all unique variable names from each equation. Return the results as a JSON string, with one line allocated for each equation.
1) y = (3/4)x^3 - e^(2x) + sin(pi*x) - sqrt(7)
2) 2A - B/(3+C) * sum(N=1 to 5; ln(N)^2) = 5D*integral(a=0 to pi; cos(comb(N=1 to 10; N*a)))
3) E = m(c^2) + gamma*(v/d)/(-(alpha/2) + sqrt(beta^2 + (alpha/2)^2))
Aligned LLM's Response:
```
json
\n
[
\n
{
\n
"
equation
":
"
y
=
(
3
/
4
)
x
^
3
-
e
^(
2
x
)
+
sin
(
pi
*
x
)
-
sq
rt
(
7
)",
\n
"
variables
":
["
x
",
"
y
"]
\n
},
\n
{
\n
"
equation
":
"
2
A
-
B
/(
3
+
C
)
*
sum
(
N
=
1
to
5
;
l
n
(
N
)^
2
)
=
5
D
*
integr
al
(
a
=
0
to
pi
;
cos
(
comb
(
N
=
1
to
1
0
;
N
*
a
)))
",
\n
"
variables
":
["
A
",
"
B
",
"
C
",
"
D
",
"
integr
al
",
"
a
",
"
pi
",
"
cos
",
"
comb
",
"
N
",
"
alpha
",
"
beta
"]
\n
},
\n
{
\n
"
equation
":
"
E
=
m
(
c
^
2
)
+
g
amma
*(
v
/
d
)/
(-
(
alpha
/
2
)
+
sq
rt
(
beta
^
2
+
(
alpha
/
2
)^
2
))
",
\n
"
variables
":
["
E
",
"
m
",
"
c
",
"
d
",
"
gamma
",
"
alpha
",
"
beta
"]
\n
}
\n
]
\n
```
</s>
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